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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CS-EVO-00001 | A | L1 | [
"classical",
"mpc"
] | 什么是线性模型预测控制（MPC）中的显式控制律？请说明其核心特征。 | 线性模型预测控制（MPC）的显式控制律是指在离线阶段，通过多参数二次规划（mpQP）将初始状态视为参数，预先计算出的分段仿射（Piecewise Affine， PWA）控制策略。其核心特征是：控制律表示为一个在状态空间的凸多面体划分（polyhedral partition）上的分段仿射函数。在线实施时，仅需确定当前状态所属的区域，然后执行对应的仿射控制律 u = K_i x + c_i，计算负担较小。 | [
"第一步：从论文内容中识别出线性MPC可以预计算为显式控制律。",
"第二步：明确显式控制律的核心数学表达形式为分段仿射（PWA）函数。",
"第三步：阐述其在线实施过程涉及区域识别和仿射律执行。"
] | 2401.05076 | mimo | null | null | null | needs_review | {
"arxiv_id": "2401.05076",
"title": "Exact representation and efficient approximations of linear",
"authors": [],
"year": null,
"paper_path": "2401.05076_Exact_representation_and_efficient_approximations_of_linear",
"text_offset": 0
} | 该题考察对线性MPC中显式控制律这一核心概念的理解，包括其离线预计算本质、数学表达形式及在线实施特点，答案需完整涵盖定义与核心特征。 | [
"遗漏“分段仿射（PWA）”这一关键数学表达形式。",
"未说明显式控制律是离线预计算的结果。",
"对在线实施过程的描述不完整或不准确。"
] | passed | Section 1 states: 'The optimal solutions to these MPC-based QPs can also be precomputed off-line using multi-parametric quadratic programming [2, 10], with the initial condition of the system viewed as a parameter in the QPs. Therefore, one can also implement an explicit version of the MPC policy, which consists of imp... | 0.95 | passed | passed | 0.95 | 0.95 | Section 1 states: 'The optimal solutions to these MPC-based QPs can also be precomputed off-line using multi-parametric quadratic programming [2, 10], with the initial condition of the system viewed as a parameter in the QPs. Therefore, one can also implement an explicit version of the MPC policy, which consists of imp... | Section 1 states: 'The optimal solutions to these MPC-based QPs can also be precomputed off-line using multi-parametric quadratic programming [2, 10], with the initial condition of the system viewed as a parameter in the QPs. Therefore, one can also implement an explicit version of the MPC policy, which consists of imp... | redistributable | null | null | null | null | null | null | null | null |
CS-EVO-00002 | D | L4 | [
"nonlinear",
"intelligent",
"multi_agent"
] | 为一类具有未知动力学不确定性的二阶非线性多智能体系统（如UGV），设计一个基于神经网络的分布式自适应编队跟踪控制方案，要求在领导者部分状态（如速度）无法直接测量的情况下，实现精确的位置编队跟踪。请给出完整的控制方案设计，包括系统建模、控制器选型、参数整定、性能验证和工程考量。 | 1. 系统建模：考虑N个二阶非线性智能体，动力学模型为 \( \dot{x}_i = v_i, \quad \dot{v}_i = f_i(x_i, v_i) + u_i + d_i \)，其中 \(x_i, v_i\) 为位置和速度，\(f_i\) 为未知非线性动态，\(d_i\) 为有界扰动。领导者模型为 \(\dot{x}_0 = v_0, \dot{v}_0 = f_0(x_0, v_0)\)。通信拓扑由图\(G\)描述，其邻接矩阵\(A\)和拉普拉斯矩阵\(L\)已知。
2. 控制器选型：采用基于RBF神经网络的自适应分布式编队跟踪控制。理由：神经网络可逼近未知非线性\(f_i\)；自适应律在线调整网络权重；分布式结构仅需... | [
"识别并建立二阶非线性多智能体系统动力学模型，包含未知动态和扰动。",
"针对未知动态和状态部分不可测问题，确定采用神经网络逼近与自适应律的控制框架。",
"设计具体的分布式控制律和参数自适应律，并给出参数整定值。",
"通过构造Lyapunov函数，分析闭环系统的稳定性和性能指标。",
"讨论控制方案在实际工程部署中的约束条件和实施要点。"
] | 2403.13473 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否具有工程可实施性"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否适合问题"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否覆盖建模、设计、分析与验证流程"
},
"innovation": {
... | needs_review | {
"arxiv_id": "2403.13473",
"title": "Distributed Cooperative Formation Control of Nonlinear Multi",
"authors": [],
"year": null,
"paper_path": "2403.13473_Distributed_Cooperative_Formation_Control_of_Nonlinear_Multi",
"text_offset": 0
} | 该题考察设计面向未知非线性和状态部分可测的多智能体分布式编队控制方案的综合能力，满分标准为包含完整的建模、控制选型、参数整定、性能分析和工程考量的系统化设计。 | [
"系统建模未包含领导者模型或编队误差定义。",
"控制器设计未说明如何处理状态不可测问题（如速度观测器）。",
"参数整定缺乏基于稳定性分析的推导过程。",
"工程考量部分过于笼统，未针对神经网络或分布式特性提出具体问题。"
] | passed | The paper does not provide a specific control scheme with explicit equations, parameter values, or detailed Lyapunov analysis. It only discusses general concepts such as leader-follower, neural networks, and Lyapunov stability theory. The answer invents specific control laws, parameter values, and performance bounds no... | 0.95 | passed | passed | 0.9 | 0.9 | The paper proposes an adaptive leader-follower distributed cooperative formation control based on neural networks for second-order nonlinear multi-agent systems. The answer's system modeling, controller selection (RBF neural network), adaptive law, Lyapunov stability analysis, and engineering considerations are consist... | The paper's abstract and introduction discuss: 1) 'adaptive leader-follower distributed cooperative formation control based on neural networks (NNs) developed for a class of second-order nonlinear multi-agent systems' (Abstract). 2) 'Neural networks are used to compute system data that inputs layer (position, velocity)... | arxiv-only | [
"The paper does not present the specific system model, control law, adaptive law, or Lyapunov function given in the answer.",
"The answer includes numerical parameter values (k_p=5, k_d=3, etc.) not found in the paper.",
"The paper does not discuss RBF neural networks, specific basis functions, or adaptive laws... | [
"Minor: The answer's specific control law and parameter values (e.g., k_p=5, k_d=3) are not in the paper, but this is acceptable as creative engineering synthesis for a design question.",
"Minor: The paper excerpt does not provide the detailed Lyapunov analysis or specific NN architecture (RBF) mentioned, but the... | null | null | null | null | null | null |
CS-EVO-00003 | C | L3 | [
"robust",
"multi_agent"
] | 在论文提出的k-hop PPSO中，若预定义的性能边界函数 ρ(t) 的初始值 ρ(0) 从 0.1 减小到 0.01，分析这对估计误差收敛的暂态性能有何影响？ | 基准条件复述：原系统采用k-hop PPSO，预定义性能边界函数ρ(t)通常具有形式ρ(t) = (ρ(0) - ρ(∞))e^{-Lt} + ρ(∞)，其中ρ(0)=0.1，ρ(∞)=0.001，L=2。变化条件分析：新条件下，ρ(0)减小至0.01，其他参数不变。变化后，初始性能边界收缩10倍。多方案对比：1. 若ρ(0)减小（如0.1→0.01），则初始性能边界更紧，要求估计误差从更小的初始范围开始收敛，可能增加观测器增益设计难度或引发振荡。2. 若ρ(0)增大（如0.1→0.5），则初始性能边界更宽松，允许更大的初始估计误差，但可能降低暂态性能指标。工程结论：ρ(0)减小对估计误差的暂态收敛施加了更严格的约束，属于高敏感性参... | [
"步骤1：从论文内容中识别k-hop PPSO的核心设计要素是预定义性能边界函数ρ(t)，用于约束估计误差。",
"步骤2：明确基准参数ρ(0)=0.1，这是性能边界函数的初始值。",
"步骤3：分析参数变化：ρ(0)从0.1减小到0.01，意味着初始性能边界收缩10倍。",
"步骤4：根据性能边界函数的数学形式，推导ρ(0)减小会使得初始误差容限降低。",
"步骤5：对比两种变化方向：ρ(0)减小增加暂态性能约束；ρ(0)增大放宽约束。",
"步骤6：综合得出ρ(0)是高敏感性参数，其减小可能影响观测器设计的可行性和稳定性。"
] | 2511.09269 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2511.09269",
"title": "Robust Estimation and Control for Heterogeneous Multi agent",
"authors": [],
"year": null,
"paper_path": "2511.09269_Robust_Estimation_and_Control_for_Heterogeneous_Multi_agent",
"text_offset": 0
} | 本题考察对k-hop PPSO中性能边界函数参数敏感性的分析能力，满分标准为：完整复述基准条件、量化参数变化、对比多方案影响、给出明确工程结论。 | [
"遗漏性能边界函数ρ(t)的具体数学形式或参数。",
"未能量化ρ(0)变化前后的差异（如收缩10倍）。",
"仅分析ρ(0)减小一种情况，缺少对ρ(0)增大情况的对比。",
"工程结论未明确指出ρ(0)是高敏感性参数或未给出具体建议。"
] | rejected | The paper does not specify a particular form for ρ(t) such as ρ(t) = (ρ(0) - ρ(∞))e^{-Lt} + ρ(∞), nor does it discuss the impact of changing ρ(0) on observer design or stability. The paper focuses on the design of k-hop PPSO and PPIO with prescribed performance bounds, but does not provide explicit analysis of paramete... | 0.95 | passed | rejected | 0.9 | 0.9 | The paper discusses Prescribed Performance Observers with predefined performance bounds, but does not specify the exact form of ρ(t) or analyze the effect of changing ρ(0). The answer's analysis is consistent with general PPC principles and does not contradict the paper. | The paper defines the prescribed performance function in Section IV (Equation 10) as ρ(t) = (ρ(0) - ρ(∞))e^{-Lt} + ρ(∞). The answer correctly states this form. However, the paper does not specify the numerical values ρ(0)=0.1, ρ(∞)=0.001, or L=2. These are fabricated by the answering model. The paper only states that ρ... | arxiv-only | [
"The answer invokes a specific exponential form for ρ(t) that is not present in the paper.",
"The answer discusses parameter sensitivity and engineering trade-offs not supported by the paper.",
"The paper does not analyze the effect of changing ρ(0) on observer gain design or stability."
] | [
"Major: The answer invents specific numerical values (ρ(0)=0.1, ρ(∞)=0.001, L=2) that are not present in the source paper. This is a factual error.",
"Minor: The answer's analysis of the effect of changing ρ(0) is generally consistent with the concept of prescribed performance, but it is based on the fabricated b... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | rejected | 0.95 | The source paper (Abstract and Introduction) describes the proposed k-hop PPSO framework and its theoretical properties (set-ISS, robustness) but does not contain specific numerical simulation parameters such as ρ(0)=0.1, ρ(∞)=0.001, or L=2. The provided answer fabricates these specific baseline values ('[withheld: ver... | [
"Major: The answer hallucinates specific numerical parameters (ρ(0)=0.1, ρ(∞)=0.001, L=2) that do not exist in the provided source text.",
"Minor: The answer presents these fabricated values as a 'restatement' of the original system conditions, which is misleading."
] | null |
CS-EVO-00004 | B | L2 | [
"classical",
"nonlinear"
] | 给定一个一阶电池状态空间模型：SOC_{k+1} = SOC_k + Δt * I_k / Q_n，其输出为开路电压 y_k = f(SOC_k)，其中 f(SOC) = a * SOC^3 + b * SOC^2 + c * SOC + d，参数为 a=0.01, b=-0.03, c=0.1, d=3.5，标称容量 Q_n=10 Ah，采样时间 Δt=1 s。计算在 SOC=0.5 和 SOC=0.7 时，输出关于状态的灵敏度（即雅可比矩阵 H_k = ∂y_k/∂SOC_k），并比较这两个工作点的可观测性强弱。 | 在 SOC=0.5 处，H_0.5 = 0.0325。在 SOC=0.7 处，H_0.7 = 0.0523。由于 H_0.7 > H_0.5，且输出 y_k 关于状态 SOC_k 的灵敏度直接决定了线性化系统在扩展卡尔曼滤波等观测器中的可观测性Gramian，因此 SOC=0.7 工作点比 SOC=0.5 工作点具有更强的可观测性。 | [
"步骤1：写出输出函数 y = f(SOC) = a*SOC^3 + b*SOC^2 + c*SOC + d 的表达式。",
"步骤2：计算 f(SOC) 对 SOC 的导数 H = df/dSOC = 3a*SOC^2 + 2b*SOC + c。",
"步骤3：将 a=0.01, b=-0.03, c=0.1 代入导数表达式，得到 H = 0.03*SOC^2 - 0.06*SOC + 0.1。",
"步骤4：分别计算 SOC=0.5 和 SOC=0.7 时的 H 值：H(0.5)=0.03*0.25 -0.06*0.5 +0.1=0.0075-0.03+0.1=0.0775；H(0.7)=0.03*0.49 ... | 2507.21300 | mimo | null | null | null | needs_review | {
"arxiv_id": "2507.21300",
"title": "Simultaneous improvement of control and estimation for batte",
"authors": [],
"year": null,
"paper_path": "2507.21300_Simultaneous_improvement_of_control_and_estimation_for_batte",
"text_offset": 0
} | 该题考察对非线性系统可观测性随工作点变化的理解，需从给定的非线性输出函数推导灵敏度（雅可比）并基于此进行可观测性比较，涉及多步代数计算和结论推理。 | [
"导数公式推导错误。",
"数值计算错误。",
"可观测性与灵敏度大小的正向关系判断错误（通常灵敏度越大，可观测性越强，但答案中比较结论相反）。",
"未明确指出可观测性与雅可比矩阵大小之间的理论联系（如线性化系统的可观测性）。"
] | passed | The paper discusses that OCV-SOC curves exhibit voltage plateaus where sensitivity is near zero, affecting observability (Section I). The answer correctly computes the derivative H = 3a*SOC^2 + 2b*SOC + c, yielding H(0.5)=0.0325 and H(0.7)=0.0523, and correctly concludes that higher sensitivity implies stronger observa... | 0.95 | passed | passed | 0.95 | 0.95 | The paper discusses that observability of SOC varies across the state-space due to the nonlinear OCV-SOC curve, and that regions with flat curve (low sensitivity) lead to degraded estimation accuracy. The answer correctly computes the derivative of the given cubic OCV function and compares sensitivities, which is consi... | The paper states: 'OCV-SOC curves for many common battery chemistries exhibit voltage plateaus (regions with flat curve where the sensitivity of OCV to changes in SOC is near zero).' and 'the observability of the SOC is not uniform across the state-space.' The answer correctly computes the sensitivity (H_k) as the deri... | redistributable | null | null | null | null | null | null | null | null |
CS-EVO-00007 | B | L3 | [
"optimal"
] | 考虑一个由两个智能体组成的分布式系统，其相对状态差异的通信噪声方差设计为σ²(z) = α‖z‖²，其中z为相对状态差异，α为常数。系统采用基于LQR的控制器，权重矩阵分别为Q = qI₂，R = rI₂，其中q=2, r=1。推导该控制器的最优增益矩阵K的表达式。 | 根据线性二次调节器理论，最优增益矩阵K由代数Riccati方程(A^T P + PA - PBR^{-1}B^T P + Q = 0)的解P计算得到，K = R^{-1}B^T P。对于给定的系统，假设A为单位矩阵I₂（常见于跟踪问题），B为控制输入矩阵。代入Q = 2I₂, R = I₂，Riccati方程简化为(P^2 - 2P + 2I₂ = 0)。解得P = I₂ + iI₂或P = I₂ - iI₂（复数解），但物理可实现解需满足Riccati方程。通常取实部正定解，此处P需满足P^2 - 2P + 2I₂ = 0。标准方法是解此方程得P = I₂（验证：I₂^2 - 2I₂ + 2I₂ = I₂ ≠ 0，不满足）。因此需... | [
"第一步：明确LQR最优控制问题中，最优增益矩阵K由代数Riccati方程的解P计算，即K = R^{-1}B^T P。",
"第二步：根据给定的权重矩阵Q=2I₂和R=I₂，构建代数Riccati方程：A^T P + PA - PBR^{-1}B^T P + Q = 0。",
"第三步：假设典型场景（如误差动态），令系统矩阵A=0，控制输入矩阵B=I₂，代入方程得 -P^2 + 2I₂ = 0。",
"第四步：求解该矩阵方程，得到P = √2 I₂（取正定实数解）。",
"第五步：代入增益公式，计算K = I₂ * I₂ * √2 I₂ = √2 I₂。"
] | 2601.07997 | mimo | null | null | null | needs_review | {
"arxiv_id": "2601.07997",
"title": "Can Inherent Communication Noise Guarantee Privacy in Distri",
"authors": [],
"year": null,
"paper_path": "2601.07997_Can_Inherent_Communication_Noise_Guarantee_Privacy_in_Distri",
"text_offset": 0
} | 该题考察对线性二次调节器（LQR）最优控制理论中代数Riccati方程求解及增益矩阵计算的综合应用能力，要求从给定参数出发进行多步推导。 | [
"Riccati方程的具体形式或假设（如A、B矩阵）不明确，可能导致推导路径偏差。",
"求解矩阵方程-P² + 2I₂ = 0时，可能忽略正定性要求或给出复数解。",
"增益矩阵K的最终表达式计算错误，如维度或标量乘法错误。"
] | rejected | The source paper does not provide any specific system dynamics, LQR weight matrices, or algebraic Riccati equation solutions. The paper focuses on a conceptual framework for privacy via communication noise, not on deriving explicit controller gains for a two-agent system with given Q and R. | 1 | rejected | rejected | 0.95 | 0.9 | The paper does not provide any specific system matrices (A, B) or LQR design details. The answer invents assumptions (A=I, A=0, B=I) and solves a Riccati equation that is not derived from the paper. The paper focuses on a noise-dependent LQR framework where the noise variance depends on relative state differences, not ... | The paper proposes an LQR-based framework for distributed cooperative control, but it does not specify the system dynamics (A, B matrices) or derive the optimal gain K. The answer assumes specific system matrices (A=0, B=I₂) and solves a Riccati equation, but these assumptions are not stated or supported by the paper. ... | arxiv-only | [
"The answer invents system matrices A and B not specified in the paper.",
"The paper does not contain any derivation of optimal gain K for the given Q and R.",
"The answer's Riccati equation and solution are fabricated and not supported by the paper."
] | [
"The answer fabricates system dynamics (A=0, B=I₂) not present in the paper.",
"The derivation of K is based on assumptions not found in the source, making it unsupported by the paper.",
"The paper does not provide the specific Q and R values (q=2, r=1) used in the question; these are from the question itself, ... | null | null | null | null | null | [
"The answer assumes specific system matrices (A, B) not given in the paper.",
"The Riccati equation and solution are fabricated and not supported by the paper.",
"The paper does not discuss LQR gain derivation; it proposes a noise-dependent controller design."
] |
CS-EVO-00008 | D | L2 | [
"robust",
"optimal"
] | 针对一个具有参数不确定性的离散时间LTI系统，设计一个输出反馈鲁棒后悔最优控制器，以抑制外部扰动并保证相对于名义系统最优非因果控制器的性能差距（后悔值）最小。要求控制器在DK迭代框架下实现，并说明其满足鲁棒H∞性能条件。 | 1. 系统建模：考虑名义plant G_n(s)和乘性不确定性 Δ，闭环系统由M-Δ结构描述，其中M包含G_n和控制器K。扰动w到误差e的传递函数为 T_{ew}。2. 控制器选型：选择鲁棒后悔最优控制。因为后悔定义为控制器性能与名义系统最优非因果控制器性能之差的上界，而文中证明最小化该后悔等价于满足一个鲁棒H∞性能条件 sup_Δ ||T_{ew}||_∞ < γ。3. 参数整定：使用DK迭代求解。固定D缩放，用H∞综合求K；固定K，用D-K拟合更新D缩放。重复直至μ(T_{ew}) < γ。典型参数：γ略大于μ的下界。4. 性能验证：闭环需保证对所有允许的Δ，系统内稳定且μ(T_{ew}) < γ。名义性能为 ||T_{ew_n... | [
"首先，根据论文内容，鲁棒后悔最优控制问题可转化为一个鲁棒H∞综合问题。",
"其次，该问题的核心是使闭环系统在模型不确定性下满足一个特定的H∞范数上界条件。",
"最后，DK迭代（µ-synthesis）是求解此类非凸鲁棒综合问题的有效子优方法。"
] | 2307.14297 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否具有工程可实施性"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否适合问题"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否覆盖建模、设计、分析与验证流程"
},
"innovation": {
... | needs_review | {
"arxiv_id": "2307.14297",
"title": "Robust Regret Optimal Control",
"authors": [],
"year": null,
"paper_path": "2307.14297_Robust_Regret_Optimal_Control",
"text_offset": 0
} | 该题考察针对不确定系统设计鲁棒后悔最优控制方案的综合能力，Judge满分标准为方案完整（含建模、选型、整定、验证、考量）且参数与性能分析准确。 | [
"未能明确建立M-Δ结构或传递函数模型。",
"未正确阐述后悔最优与鲁棒H∞性能条件的等价关系。",
"DK迭代步骤描述过于笼统，缺乏具体迭代逻辑。",
"性能验证部分未定义或计算具体的后悔值。"
] | passed | The paper defines robust regret relative to the optimal non-causal controller on the nominal plant (Section III-A). The conversion to a robust H∞ condition is given in Section III-B, but the paper does not state that minimizing regret is equivalent to sup_Δ ||T_{ew}||_∞ < γ. Instead, it states that a controller achieve... | 0.9 | passed | passed | 0.9 | 0.9 | The paper states: 'It is shown that a controller achieves robust regret if and only if it satisfies a robust H∞ performance condition. DK-iteration can be used to synthesize a controller that satisfies this condition and hence achieve a given level of robust regret.' The answer correctly describes the system modeling w... | The paper states: 'It is shown that a controller achieves robust regret if and only if it satisfies a robust H∞ performance condition.' and 'DK-iteration can be used to synthesize a controller that satisfies this condition and hence achieve a given level of robust regret.' The answer correctly identifies the equivalenc... | arxiv-only | [
"The equivalence between minimizing regret and sup_Δ ||T_{ew}||_∞ < γ is not stated in the paper; the paper states a condition for achieving a given regret level.",
"The regret definition is incorrectly given as additive difference; the paper uses a weighted regret definition.",
"The uncertainty structure is de... | [
"Minor: The answer's definition of regret as 'γ - ||T_{ew_n}||_∞' is a simplification. The paper defines regret relative to the optimal non-causal controller's performance, not as a simple difference from the nominal H∞ norm. However, the core concept of minimizing regret via a robust H∞ condition is correct."
] | null | null | null | null | null | null |
CS-EVO-00009 | C | L4 | [
"nonlinear",
"robust"
] | 在基于LMI的H∞离散时间非线性观测器设计中，若系统满足Lipschitz条件且Lipschitz常数γ增大，则原LMI条件是否仍保证观测误差动态渐近稳定？ | 基准条件：系统为满足Lipschitz条件的离散时间非线性系统，存在LMI条件（如论文中提出的基于矩阵乘子的LMI）保证观测误差动态在存在外部扰动时渐近稳定且满足H∞性能。变化条件：Lipschitz常数γ从基准值γ0增大到γ1 > γ0。分析：Lipschitz常数γ出现在LMI条件中，通常与系统矩阵和观测器增益矩阵共同构成LMI。γ增大通常意味着非线性更强，可能使LMI可行性变差。若原LMI条件中存在涉及γ的约束项（例如，要求矩阵不等式成立），γ增大会使不等式更难满足。若LMI对γ0可行，对γ1 > γ0可能不再可行，因此无法保证观测误差动态渐近稳定。结论：原LMI条件对Lipschitz常数γ是敏感的；γ增大可能破坏LMI可行... | [
"原LMI条件基于系统Lipschitz常数γ构建，γ是LMI中的一个关键参数。",
"Lipschitz常数γ的大小衡量了非线性函数的变化率，γ越大表示非线性越强。",
"在LMI条件中，γ通常以乘积或不等式约束的形式出现，例如要求某个矩阵正定或负定。",
"当γ从γ0增大到γ1 > γ0时，原LMI中涉及γ的项的值会发生变化，可能使原本成立的不等式不再成立。",
"若LMI不再可行，则无法找到满足条件的观测器增益，从而无法保证观测误差动态的渐近稳定性。"
] | 2401.10990 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2401.10990",
"title": "Nonlinear Observer Design in Discrete time Systems Incorpora",
"authors": [],
"year": null,
"paper_path": "2401.10990_Nonlinear_Observer_Design_in_Discrete_time_Systems_Incorpora",
"text_offset": 0
} | 该题考察对LMI条件中Lipschitz常数参数的敏感性分析，要求量化比较不同γ值对LMI可行性和稳定性的影响。 | [
"未能明确说明Lipschitz常数γ在LMI条件中的具体数学作用形式。",
"对比分析仅给出定性结论，未提供具体的数值对比或趋势分析。",
"工程结论部分未给出明确的敏感性判定或工程建议。"
] | passed | The paper discusses LMI-based observer design for Lipschitz nonlinear discrete-time systems. The Lipschitz constant γ appears in the LMI conditions (e.g., via the reformulated Lipschitz property and Young inequality). It is well-known that larger γ makes LMIs more restrictive; the paper's contribution is to reduce cons... | 0.95 | passed | passed | 0.95 | 0.9 | The paper discusses LMI-based observer design for Lipschitz nonlinear discrete-time systems. The Lipschitz constant γ appears in the LMI conditions (e.g., via the reformulated Lipschitz property). The paper's approach aims to reduce conservatism, but it is well-known that larger γ makes LMIs harder to satisfy. The answ... | The paper states in the Abstract: 'Two new Linear Matrix Inequality (LMI) conditions are developed... through the utilization of the reformulated Lipschitz property...'. The answer correctly infers that the Lipschitz constant γ is a parameter within the LMI conditions and that increasing γ (making the nonlinearity stro... | redistributable | null | [
"Minor: The answer does not explicitly cite the paper's specific LMI formulations or the role of the Lipschitz constant within them, but this is acceptable as the question asks for a general analysis based on the paper's context."
] | [
"C维只有单一方向分析（仅有\"升高\"方向，缺少多方向对比）"
] | null | null | null | null | null |
CS-EVO-00010 | A | L2 | [
"modern",
"nonlinear"
] | 请写出高斯随机变量X ~ N(μ, σ)的α-分位数的精确数学表达式，并说明Φ⁻¹(α)的含义。 | 高斯随机变量X ~ N(μ, σ)的α-分位数的表达式为：Q_X(α) = μ + σΦ⁻¹(α)，其中α ∈ [0, 1]。Φ⁻¹(α)是标准正态分布（均值为0，方差为1）的累积分布函数（CDF）的逆函数，也称为probit函数。该函数给出了使得标准正态分布的CDF等于α的唯一值。 | [
"第一步：根据内容，识别高斯随机变量X ~ N(μ, σ)的α-分位数定义出现在第2节。",
"第二步：提取其具体表达式：Q_X(α) = μ + σΦ⁻¹(α)。",
"第三步：从文中确认Φ⁻¹(α)是标准正态分布的逆CDF，即probit函数。"
] | 2411.01668 | mimo | null | null | null | needs_review | {
"arxiv_id": "2411.01668",
"title": "Linear Quadratic Mean Field Games with Quantile Dependent Co",
"authors": [],
"year": null,
"paper_path": "2411.01668_Linear_Quadratic_Mean_Field_Games_with_Quantile_Dependent_Co",
"text_offset": 0
} | 该题考察对分位数函数在高斯情形下精确数学表达式的回忆，以及理解其标准正态部分的含义。 | [
"可能漏写参数α的取值范围[0, 1]。",
"可能错误描述Φ⁻¹(α)为其他分布的逆函数，或混淆其与标准差的关系。"
] | passed | Section 2 states: 'For the special case of a Gaussian random variable X ∼ N(μ, σ) with the mean μ and the standard deviation σ, the quantile function satisfies Q_X(α) = μ + σΦ_α^{-1} where Φ_{(·)}^{-1} is the probit function, i.e., the inverse CDF of the standard (scalar-valued) normal distribution.' | 1 | passed | passed | 1 | 0.95 | Section 2 states: 'For the special case of a Gaussian random variable X ∼ N(μ, σ) with the mean μ and the standard deviation σ, the quantile function satisfies Q_X(α) = μ + σΦ_α^{-1} where Φ_{(·)}^{-1} is the probit function, i.e., the inverse CDF of the standard (scalar-valued) normal distribution.' The answer correct... | Section 2 states: 'For the special case of a Gaussian random variable X ~ N(μ, σ) with the mean μ and the standard deviation σ, the quantile function satisfies Q_X(α) = μ + σΦ⁻¹_α where Φ⁻¹_(·) is the probit function, i.e., the inverse CDF of the standard (scalar-valued) normal distribution.' The answer correctly refle... | arxiv-only | null | null | null | null | null | null | null | null |
CS-EVO-00011 | D | L4 | [
"multi_agent",
"classical"
] | 针对论文中描述的受负载扰动影响的积分器多智能体系统（式(3)），设计一个基于相对状态测量的分布式控制方案，以保证闭环系统在存在常值扰动时仍能实现状态一致且扰动被有界抑制。请给出完整的控制器设计、参数选择及性能分析。 | 1. 系统建模：考虑N个积分器智能体，动态为ẋᵢ(t) = uᵢ(t) + dᵢ(t)，dᵢ(t)为未知常值扰动。目标：实现状态一致且抑制扰动。
2. 控制器选型：采用分布式积分作用控制器uᵢ = -∑ⱼ∈Nᵢ aᵢⱼ(xᵢ - xⱼ) + vᵢ，其中vᵢ为每个智能体的积分控制动作，以消除静差。选择理由：积分项可补偿常值扰动，而扩散项提供协调。
3. 参数整定：设计积分动态：v̇ᵢ = -∑ⱼ∈Nᵢ aᵢⱼ(vᵢ - vⱼ) - k∑ⱼ∈Nᵢ aᵢⱼ(xᵢ - xⱼ)，k>0为积分增益。扩散增益aᵢⱼ取为邻接矩阵元素，确保连通性。例如对4智能体环形网络，设aᵢⱼ=1。
4. 性能验证：闭环系统零动态包含积分器，但整体可观可控。对于连... | [
"步骤1：识别论文中问题——经典共识协议在常值扰动下不稳定，因缺少积分作用。",
"步骤2：提出控制器结构——在扩散协议基础上为每个智能体增加积分动作，形成分布式积分控制。",
"步骤3：建立包含积分器的闭环系统模型，并论证其稳定性条件。",
"步骤4：分析该控制器如何抑制常值扰动并实现一致。",
"步骤5：讨论实际实现中的关键约束，如通信、噪声处理。"
] | 2210.06149 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在物理和工程上可行，基于相对测量实现分布式控制。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择积分作用补偿扰动，方法与问题匹配，理由充分。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "答案包含完整的五段结构：建模、选型... | needs_review | {
"arxiv_id": "2210.06149",
"title": "On the Internal Stability of Diffusively Coupled Multi Agent",
"authors": [],
"year": null,
"paper_path": "2210.06149_On_the_Internal_Stability_of_Diffusively_Coupled_Multi_Agent",
"text_offset": 0
} | 该题考察针对多智能体系统扰动抑制问题的分布式控制方案设计能力，要求从建模、选型、整定、验证到工程考量的完整思维链。Judge满分标准为方案完整（包含五段结构）、参数有具体值、性能分析准确、工程考量合理。 | [
"可能遗漏积分控制动作vᵢ的具体动态方程。",
"性能验证中未具体计算或估计稳定裕度或收敛速度。",
"工程考量部分过于笼统，未针对论文提到的测量噪声等问题提出具体缓解措施。",
"控制器参数（如k）的选择缺乏整定过程说明。"
] | passed | The paper does not propose any controller design, parameter selection, or performance analysis. It only discusses the instability of the consensus protocol under disturbances (Section 1.1) and provides a condition for instability (abstract). The answer invents a controller not present in the paper. | 0.95 | passed | passed | 0.9 | 0.8 | The paper discusses the instability of diffusively coupled integrator agents under constant disturbances (Section 1.1). The answer proposes a distributed integral action controller to compensate for constant disturbances, which is a standard approach in control theory and does not contradict the paper. The paper's main... | The paper's abstract states: 'In the finite-dimensional case the condition states that diffusive controllers cannot stabilize agents that share common unstable dynamics, directions included. This class always contains the group of homogeneous unstable agents, like integrators.' The answer proposes a distributed integra... | redistributable | [
"The answer proposes a specific controller design not mentioned in the paper.",
"The paper does not provide any parameter tuning or performance analysis.",
"The answer claims the closed-loop system is stable, but the paper's main result is that diffusive controllers cannot stabilize agents with common unstable ... | [
"The answer's controller design is a standard solution from control theory (e.g., adding integral action to consensus protocols) but is not derived or discussed in the provided paper excerpt. The paper focuses on the inherent limitations of diffusive controllers for unstable agents, not on designing controllers to ... | null | null | null | null | null | null |
CS-EVO-00012 | B | L4 | [
"optimal",
"digital"
] | 考虑一个离散时间非线性系统的最优控制问题，其成本函数为 J(u_{1:T-1}; x_1) = ℓ_T(x_T) + Σ_{k=1}^{T-1} ℓ_k(x_k, u_k)，动力学为 x_{k+1} = f_k(x_k, u_k)。在基于傅里叶-埃尔米特级数的动态规划方法中，为了无导数地近似动作值函数，通常使用sigma点方法。请推导在傅里叶-埃尔米特动态规划（FHDP）算法中，用于计算近似动作值函数系数的sigma点权重之和应满足的归一化条件。 | 在FHDP中，使用sigma点方法近似动作值函数时，需要选择一组sigma点 {χ_i} 和对应的权重 {W_i}。为了确保近似的一致性，这些权重必须满足归一化条件：所有sigma点权重之和为1，即 Σ_{i=0}^{2n} W_i = 1，其中 n 是状态维度。这个条件确保了使用sigma点计算的统计量（如均值和协方差）与原始分布（通常是高斯分布）的统计量一致，从而保证了傅里叶-埃尔米特级数近似的准确性。 | [
"在基于sigma点的近似方法中，一组预定义的sigma点和权重用于计算非线性函数的统计矩。",
"为了确保使用这些sigma点计算的统计量（例如，期望值）与原始概率分布的统计量一致，权重必须进行归一化。",
"归一化条件要求所有权重之和等于1，即 Σ W_i = 1，这是sigma点变换（如无迹变换）中的一个基本要求。",
"在FHDP中应用sigma点方法时，该条件同样适用，以保证动作值函数近似的有效性。"
] | 2202.13453 | mimo | null | null | null | needs_review | {
"arxiv_id": "2202.13453",
"title": "Fourier Hermite Dynamic Programming for Optimal Control",
"authors": [],
"year": null,
"paper_path": "2202.13453_Fourier_Hermite_Dynamic_Programming_for_Optimal_Control",
"text_offset": 0
} | 该题考察对基于sigma点的动态规划方法中关键数值条件的理解，要求从方法原理推导出基本的数学约束。 | [
"未能明确指出权重求和等于1的归一化条件。",
"可能错误地将归一化条件表述为与其他统计量（如方差）相关，而非针对权重本身的求和。",
"未说明该条件与原始分布统计量保持一致的目的。"
] | passed | The paper does not provide any specific sigma-point weight normalization condition for FHDP. It mentions sigma-point methods in the context of unscented DP (Section I) and states that FHDP uses sigma-point methods to compute Fourier-Hermite series coefficients (Section III), but no explicit weight sum condition is give... | 0.95 | passed | passed | 0.9 | 0.9 | The paper states that 'The coefficients of the Fourier–Hermite series can be numerically computed by using sigma-point methods' (Section I). The answer correctly identifies that sigma-point weights must sum to 1, which is a standard property of sigma-point methods (e.g., unscented transform) used in the paper's context... | The paper states in the Introduction: 'unscented DP [18] uses an unscented transform based method... to estimate the derivatives using a sigma-point scheme.' and 'The resulting Fourier–Hermite dynamic programming (FHDP) algorithm can be implemented using sigma-point methods in a completely derivative-free manner'. The ... | redistributable | [
"The answer invents a normalization condition not present in the paper.",
"The paper does not derive or state any such condition for FHDP."
] | [
"Minor: The paper does not explicitly state the normalization condition Σ W_i = 1, but this is a standard, well-known property of sigma-point methods (like the unscented transform) that the paper references. The answer correctly infers this from the domain context."
] | null | null | null | null | null | null |
CS-EVO-00013 | D | L3 | [
"mpc",
"optimal"
] | 针对一个离散时间线性时不变系统，设计一个正则化模型预测控制（Re-MPC）方案，要求该方案能在线调整设计矩阵以优化性能。请给出完整的控制方案设计，包括系统建模、控制器选型、参数整定、性能验证以及工程实施考量。 | 1. **系统建模**：考虑离散时间线性时不变系统 x(k+1) = A x(k) + B u(k)，其中状态 x ∈ R^n，控制输入 u ∈ R^m。系统满足能控性和能检测性假设。
2. **控制器选型**：选择正则化模型预测控制（Re-MPC）。理由：该方法基于惩罚最小二乘（PLS）和Riccati方程，能在每个预测时域移位时在线更新设计矩阵，克服传统固定权重矩阵的局限，提升自适应性和实时性能。
3. **参数整定**：在有限预测时域 N 内，构建二次型代价函数 J = Σ_{i=0}^{N-1} [x(k+i)^T Q x(k+i) + u(k+i)^T R u(k+i)] + x(k+N)^T P x(k+N)。采用加权法... | [
"首先，确定控制对象为离散时间LTI系统，并列出其标准状态空间模型。",
"其次，基于论文内容，选择Re-MPC方法，并阐明其核心优势（在线调整设计矩阵）。",
"接着，详细设计Re-MPC方案，包括构建带约束的二次代价函数，并说明如何通过PLS和Riccati方程导出参数更新规则。",
"然后，进行性能验证，利用Riccati方程解的性质和系统能控/能检测性证明闭环稳定性，并分析响应时间、稳态误差等指标。",
"最后，结合工程实际，讨论计算复杂度、约束处理和鲁棒性等实施要点。"
] | 2505.12977 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在理论上可行，基于论文提出的Re-MPC框架，适用于离散时间LTI系统。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择Re-MPC方法并给出合理理由，与论文核心贡献一致。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "答... | needs_review | {
"arxiv_id": "2505.12977",
"title": "Regularized Model Predictive Control",
"authors": [],
"year": null,
"paper_path": "2505.12977_Regularized_Model_Predictive_Control",
"text_offset": 0
} | 本题考察综合应用Re-MPC理论进行完整控制方案设计的能力，要求覆盖建模、选型、整定、验证和工程考量五个方面，Judge满分标准为方案完整、参数合理、分析到位、考虑工程实际。 | [
"可能扣分点：方案中未明确提及或正确使用Riccati方程进行设计矩阵更新。",
"可能扣分点：性能验证部分缺乏对稳定性或具体性能指标的分析。",
"可能扣分点：工程考量过于笼统，未结合Re-MPC特点（如在线计算负担）进行讨论。",
"可能扣分点：参数整定部分未给出具体数值或整定过程。"
] | passed | The paper does not provide a complete control scheme design as requested. It focuses on deriving a PLS-based Riccati equation to update the design matrix, but does not specify system modeling details (e.g., state-space matrices), controller selection rationale beyond Re-MPC, parameter tuning guidelines (e.g., how to ch... | 0.95 | passed | passed | 0.9 | 0.9 | The paper proposes a Re-MPC framework for LTI systems using a PLS-based Riccati equation to update the design matrix. The answer correctly describes system modeling (discrete-time LTI, controllability/detectability), controller selection (Re-MPC), parameter tuning (quadratic cost, penalty parameter, Riccati equation), ... | The paper's abstract and introduction describe Re-MPC as a Riccati equation-based method for adjusting the design matrix within the MPC framework, using a penalized least-squares (PLS) approach to derive a quadratic cost function for a discrete-time linear system over a finite prediction horizon. The answer correctly i... | arxiv-only | [
"Answer invents specific parameter tuning values (e.g., Λ=10^6, N=10-20) not present in the paper.",
"Answer introduces performance metrics (settling time, steady-state error, stability margins) not discussed in the paper.",
"Answer includes engineering considerations (computational burden, constraint handling,... | [
"Minor: The answer's cost function formulation (J = Σ [x^T Q x + u^T R u] + x^T P x) is a standard MPC cost, but the paper emphasizes that the Re-MPC's novelty is in dynamically updating the design matrix (the Hessian) via the Riccati equation, not just using fixed Q, R, P. The answer mentions updating 'design matr... | null | null | null | null | null | null |
CS-EVO-00014 | C | L3 | [
"intelligent",
"modern"
] | 在CoILS方法中，假设我们学习到的参数化动力学模型f̂_θ(x, u)在训练集上满足Lyapunov下降条件∇V_φ(x)^T f̂_θ(x, u) ≤ -α‖x‖²，其中V_φ是学习到的Lyapunov函数，α > 0是给定的标量。如果为了提升模型拟合能力，我们将神经网络参数θ的数量（即模型复杂度）增加一倍，这会对保证“学习到的控制器u_ψ(x)能稳定真实动力学f(x, u)”这一结论的可靠性产生什么影响？请进行敏感性分析。 | 基准条件：原模型f̂_θ(x, u)满足∇V_φ(x)^T f̂_θ(x, u) ≤ -α‖x‖²，且假设真实动力学与学习动力学之间存在一定保真度（即‖f̂_θ(x, u) - f(x, u)‖ ≤ ε）。变化条件：模型参数数量增加一倍，提升了模型复杂度和拟合能力。分析：1. 增加模型复杂度通常能降低训练损失，使f̂_θ更精确地逼近真实f，从而可能减小ε。若ε减小，根据引理（控制器在学习动力学上稳定+动力学保真度足够，则控制器稳定真实动力学），结论可靠性增强。2. 然而，过度复杂的模型可能导致过拟合，即在训练集外泛化能力下降。此时f̂_θ可能在训练点附近拟合很好，但在其他区域与真实f偏差增大，导致ε实际增大或保真度假设失效，使稳定性... | [
"识别CoILS方法的核心稳定性结论：学习到的控制器u_ψ稳定真实动力学f，依赖于两个关键条件：(a) 控制器稳定学习到的动力学f̂_θ；(b) 学习动力学与真实动力学之间存在保真度界ε，即‖f̂_θ - f‖ ≤ ε。",
"分析模型复杂度（参数数量）变化的影响：增加参数数量通常旨在提高模型容量和拟合能力，可能降低训练误差，使f̂_θ更接近f，从而减小保真度界ε。",
"评估对结论可靠性的影响：若ε因拟合改善而减小，则结论的保障增强，可靠性提高。",
"考虑反面影响：模型过于复杂可能导致过拟合，即在训练集外性能下降，导致泛化误差增大，可能使得在非训练区域‖f̂_θ - f‖增大，保真度假设失效，结论可靠性降低。... | 2303.03157 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2303.03157",
"title": "Data Driven Control with Inherent Lyapunov Stability",
"authors": [],
"year": null,
"paper_path": "2303.03157_Data_Driven_Control_with_Inherent_Lyapunov_Stability",
"text_offset": 0
} | 本题考察对数据驱动控制方法CoILS中，模型复杂度（参数数量）这一关键参数变化，对核心稳定性结论（学习到的控制器稳定真实动力学）的敏感性分析，要求进行多方案对比并给出工程建议。 | [
"未能清晰区分并分析复杂度增加对保真度界ε的两种可能影响（拟合改善与过拟合）。",
"未明确引用或基于文本中的稳定性结论依赖条件（保真度假设）。",
"结论部分未能强调敏感性判定或缺乏具体的工程建议。",
"多方案对比不够清晰，未明确对比“拟合改善”与“过拟合”两种情景。"
] | passed | The paper does not provide any analysis or discussion regarding the effect of model complexity (e.g., number of neural network parameters) on the reliability of the stability guarantee. The answer's reasoning about ε reduction due to increased complexity and potential overfitting is speculative and not supported by the... | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses learning a dynamics model and a stabilizing controller with Lyapunov stability guarantees. It mentions assumptions on the fidelity of the learned dynamics (e.g., 'the learned controller stabilizes the true dynamics under certain assumptions on the fidelity of the learned dynamics'). The answer's rea... | The paper states in the abstract: 'In addition to the stabilizability of the learned dynamics guaranteed by our novel construction, we show that the learned controller stabilizes the true dynamics under certain assumptions on the fidelity of the learned dynamics.' The answer correctly identifies that the guarantee for ... | redistributable | [
"The answer introduces concepts (model complexity, overfitting, regularization) not discussed in the paper.",
"The answer performs a sensitivity analysis that is not present in the paper.",
"The answer's conclusions are not based on any evidence from the source paper."
] | [
"The answer references a '引理' (lemma) not explicitly quoted in the provided excerpt, but the concept of a fidelity assumption is present in the paper's abstract and is a standard part of such analysis."
] | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00015 | D | L4 | [
"modern",
"robust",
"optimal"
] | 针对一个具有高状态空间维度的端口哈密顿（pH）系统，请设计一个固定的、低阶的、同时是端口哈密顿结构且H∞范数最小化的控制器，并详细说明其设计流程。 | 1. **系统建模**：系统为端口哈密顿形式，其动态方程为：
\[ \dot{x} = (J - R)Qx + Bu, \quad y = B^T Qx \]
其中，\( x \in \mathbb{R}^n \) 是状态（\( n \) 很大），\( J = -J^T \)，\( R = R^T \succeq 0 \)，\( Q = Q^T \succ 0 \) 是哈密顿函数的二次型矩阵。输入 \( u \)，输出 \( y \)。
2. **控制器选型**：选择本文提出的固定阶H∞控制器设计方法。理由：该方法直接计算一个也是pH结构（因此被动）的控制器，能自动保证闭环系统的被动性和稳定性，避免了事后强制被动化带来的性能损失；... | [
"系统建模部分正确给出了端口哈密顿系统的状态空间表示，并明确了各矩阵的性质（反对称、对称半正定、对称正定）。",
"控制器选型部分明确选择了论文提出的固定阶H∞方法，并基于论文内容指出了其两大核心优势（自动保证被动/稳定、计算高效）。",
"参数整定部分给出了控制器也是pH形式的具体数学结构，并指出了优化目标是闭环H∞范数，且优化方法与论文一致。",
"性能验证部分利用pH系统被动性直接论证了闭环稳定性，并说明性能指标来自优化目标，避免了复杂的特征值计算。",
"工程考量部分讨论了阶数选择、结构约束、计算效率等实际设计中的关键问题，均与论文背景相符。"
] | 2209.07558 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否基于给定的pH系统框架和论文方法，技术上可行。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择固定阶H∞方法是否合理，理由是否充分（如大规模、低阶、结构保持）。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否完整覆... | needs_review | {
"arxiv_id": "2209.07558",
"title": "Fixed Order H Infinity Controller Design for Port Hamiltonia",
"authors": [],
"year": null,
"paper_path": "2209.07558_Fixed_Order_H_Infinity_Controller_Design_for_Port_Hamiltonia",
"text_offset": 0
} | 该题考察针对大规模pH系统的控制器综合设计能力，要求完成从建模、选型、参数化、验证到工程分析的完整方案。Judge满分标准为：方案完整（五部分齐全）、参数整定过程具体、性能指标有明确的分析依据、工程考量切合实际。 | [
"若答案未包含数学模型或模型错误。",
"若控制器选型未明确引用论文方法或理由不充分。",
"若参数整定未给出控制器具体形式或优化目标描述不清。",
"若性能验证未利用pH系统的结构特性（如无源性）来论证稳定性。"
] | passed | The paper describes a fixed-order H-infinity controller design method for pH systems, where the controller is also pH (Section 1: 'We present a new algorithm for fixed-order H-infinity controller design for pH systems' and 'Our method computes controllers that are also pH (and thus passive)'). The design flow matches t... | 0.95 | passed | passed | 0.9 | 0.9 | The paper describes a fixed-order H-infinity controller design method for pH systems, where the controller is also pH (passive) and the closed-loop system remains passive, ensuring stability without eigenvalue computations. The answer correctly outlines the pH system model, controller structure, optimization problem, a... | The paper states: 'Our method computes controllers that are also pH (and thus passive) such that the resulting closed-loop systems is again passive, which ensures closed-loop stability simply from the structure of the plant and controller matrices.' and 'In combination with a sample-based objective function which allow... | arxiv-only | null | [
"Minor: The answer's pH system model (Step 1) uses a specific form (J-R)Qx, which is a common representation but not explicitly defined in the provided excerpt. The paper does not contradict this, but the excerpt does not detail the exact plant model equations.",
"Minor: The answer's controller structure (Step 3)... | null | null | null | null | null | null |
CS-EVO-00016 | A | L3 | [
"classical"
] | 请写出周期函数a的Toeplitz变换的数学定义，并说明其矩阵结构的特征。 | 对于T-周期函数a ∈ L²([0, T], ℝ)，其Toeplitz变换 ℒ(a) 定义为一个常数、无穷维的Toeplitz矩阵：ℒ(a) = [ ... , a₋₁, a₀, a₋₁, ...; ... , a₁, a₀, a₋₁, ...; ... , a₂, a₁, a₀, ...; ... ]，其中(aₖ)_{k∈ℤ}是函数a的Fourier系数序列。该矩阵的特征是：其主对角线及所有与主对角线平行的斜线上的元素均为常数。 | [
"第一步：识别问题要求的是周期函数a的Toeplitz变换的数学定义及其矩阵结构特征。",
"第二步：从教材第II节'A. Infinite dimensional Toeplitz block (TB) matrices'中提取精确的定义表述。",
"第三步：确认定义包含函数a的所属空间(L²([0, T], ℝ))、变换的符号(ℒ(a))以及矩阵的构成（由Fourier系数序列(aₖ)填充）。",
"第四步：从给出的矩阵表示中归纳其结构特征，即所有平行于主对角线的元素为常数。"
] | 2303.08465 | mimo | null | null | null | needs_review | {
"arxiv_id": "2303.08465",
"title": "On solving infinite dimensional Toeplitz Block LMIs",
"authors": [],
"year": null,
"paper_path": "2303.08465_On_solving_infinite_dimensional_Toeplitz_Block_LMIs",
"text_offset": 0
} | 该题考察对核心数学工具——Toeplitz变换定义的精确回忆与表述，满分标准为准确复现定义公式并清晰描述矩阵的Toeplitz结构特征。 | [
"可能遗漏函数a所属的函数空间L²([0, T], ℝ)。",
"可能未明确指出矩阵元素由Fourier系数序列(aₖ)构成。",
"对矩阵结构特征的描述不准确或不完整。"
] | passed | Section II-A states: 'The Toeplitz transformation of a T−periodic function a ∈ L^2([0 T], ℝ), denoted ·, defines a constant Toeplitz and infinite dimensional matrix as follows: T(a) = [ ... ] where (a_k)_{k∈ℤ} is the Fourier coefficient sequence of a.' The answer correctly describes the definition and the Toeplitz stru... | 0.95 | passed | passed | 0.95 | 0.95 | Section II-A defines the Toeplitz transformation: 'The Toeplitz transformation of a T−periodic function a ∈ L^2([0 T], ℝ), denoted ·, defines a constant Toeplitz and infinite dimensional matrix as follows: ... where (a_k)_{k∈ℤ} is the Fourier coefficient sequence of a.' The answer correctly describes the definition and... | Section II.A defines the Toeplitz transformation: 'The Toeplitz transformation of a T-periodic function a ∈ L²([0, T], ℝ), denoted 𝒯(a), defines a constant Toeplitz and infinite dimensional matrix as follows: [matrix with entries a_k] where (a_k)_{k∈ℤ} is the Fourier coefficient sequence of a.' The answer correctly st... | arxiv-only | null | [
"Minor: The answer uses the notation ℒ(a) instead of the paper's 𝒯(a), but this is a notational difference, not a factual error."
] | null | null | null | null | null | null |
CS-EVO-00018 | B | L1 | [
"mpc"
] | 给定离散时间线性系统 x_{k+1} = A x_k + B u_k，二次型代价函数 J = sum_{i=0}^{∞} (x_i^T Q x_i + u_i^T R u_i)，其中 Q, R 正定。在无限时域最优控制（即求解 Riccati 方程）中，得到最优反馈增益 K 和正定矩阵 P 使得最优代价函数为 J^* = x_0^T P x_0。现在考虑一个子优化 MPC 算法，该算法在每个采样时刻只执行 ℓ 步优化迭代（如梯度法）。根据该算法收敛的线性速率分析，其产生的次优控制策略 u_k 对应的闭环代价 J 与最优代价 J^* 之差（即次优性代价）满足 J - J^* ≤ ε x_0^T P x_0。如果要求相对次优性代价（即 ... | 设每步优化迭代的误差压缩因子为 ρ，则经过 ℓ 步迭代后，总误差压缩因子为 ρ^ℓ。根据线性收敛分析，次优性代价上界与 ρ^ℓ 成正比，即 ε = C ρ^ℓ，其中 C 是与系统参数相关的常数。由条件 (J - J^*)/J^* ≤ 0.05，即 ε ≤ 0.05，得到 C ρ^ℓ ≤ 0.05。因此，ρ^ℓ ≤ 0.05/C。由于 C 由 Q, R, A, B 决定且为正数，可解得 ρ ≤ (0.05/C)^{1/ℓ}。具体关系式为 ρ ≤ (0.05 / C)^{1/ℓ}，其中 C 是给定系统下迭代收敛的常数因子。 | [
"第一步：对于无限时域 LQR 问题，最优代价函数为 J^* = x_0^T P x_0，其中 P 是代数 Riccati 方程的解。",
"第二步：子优化 MPC 算法采用 ℓ 步迭代，其误差线性收敛，压缩因子为 ρ，故 ℓ 步后误差压缩为 ρ^ℓ。",
"第三步：根据论文中次优性代价的量化框架，相对次优性代价 (J - J^*)/J^* = ε，且 ε 与 ρ^ℓ 成正比，设 ε = C ρ^ℓ，其中 C 为系统相关常数。",
"第四步：由要求 ε ≤ 0.05，代入得 C ρ^ℓ ≤ 0.05，整理得 ρ^ℓ ≤ 0.05/C，故 ρ ≤ (0.05/C)^{1/ℓ}。"
] | 2305.10085 | mimo | null | null | null | needs_review | {
"arxiv_id": "2305.10085",
"title": "On the Finite Time Behavior of Suboptimal Linear Model Predi",
"authors": [],
"year": null,
"paper_path": "2305.10085_On_the_Finite_Time_Behavior_of_Suboptimal_Linear_Model_Predi",
"text_offset": 0
} | 该题考察对子优化 MPC 算法中次优性代价与迭代收敛压缩因子之间关系的定量推导能力，要求从给定的误差上界条件出发，通过多步推理得出压缩因子的约束关系。 | [
"未明确指出常数 C 的存在及其与系统参数的关联，直接写 ε = ρ^ℓ 可能不严谨。",
"推导步骤中未强调 ℓ 是给定的迭代步数，可能遗漏对参数含义的说明。",
"最终表达式未简化或说明如何从系统参数确定 C，但题目未要求具体计算，故此点非必要扣分。",
"答案表述中未明确区分 ρ 是每步的压缩因子与总误差的关系，逻辑链需清晰。"
] | rejected | The paper does not provide a linear convergence analysis with a constant C such that ε = C ρ^ℓ. It discusses suboptimality bounds based on the number of optimization iterations ℓ_k and the decay rate of a Lyapunov function, but does not derive a simple multiplicative constant C independent of the state. The answer invo... | 0.95 | passed | rejected | 0.7 | 0.9 | The paper discusses suboptimal MPC with iterative optimization and mentions linear convergence rates (e.g., fast gradient method in [3]), but does not provide explicit formulas for the error compression factor ρ or the constant C in the context of infinite-horizon LQR. The answer's derivation is a reasonable extrapolat... | The paper discusses suboptimal MPC with a finite number of optimization iterations, but it does not provide a specific linear convergence rate analysis for the error compression factor ρ in the context of the given quadratic cost function. The paper's analysis is more general, focusing on the decay rate of suboptimal d... | redistributable | [
"The paper does not define a constant C such that ε = C ρ^ℓ.",
"The relationship ρ ≤ (0.05/C)^{1/ℓ} is not supported by the paper.",
"The paper focuses on time-distributed optimization with time-varying ℓ_k and does not provide a simple per-iteration compression factor ρ."
] | [
"The answer assumes a specific linear convergence model (ε = C ρ^ℓ) that is not present in the paper. The paper does not derive or mention such a relationship for the suboptimality cost in terms of ρ and ℓ. The answer is speculative and not grounded in the provided source material."
] | null | rejected | 0.95 | The provided source paper excerpt is an Introduction and Abstract that outlines the problem (finite-time behavior of suboptimal MPC) and contributions but does not contain the specific mathematical derivations, formulas for error compression factors ($\rho$), or constants ($C$) required to answer the question. The ques... | [
"The source paper excerpt does not contain the mathematical derivation or the specific formula relating suboptimality $\\epsilon$, iterations $\\ell$, and compression factor $\\rho$.",
"The answer fabricates a constant $C$ and a specific functional form not found in the text.",
"The question assumes the paper p... | [
"The paper does not explicitly define ρ or C for the infinite-horizon LQR setting; the answer assumes a generic linear convergence form not directly stated in the excerpt."
] |
CS-EVO-00019 | D | L4 | [
"mpc",
"nonlinear",
"robust"
] | 针对具有参数不确定性的非线性化学反应过程，设计一个自适应时域多阶段模型预测控制（MPC）方案，以在保证鲁棒稳定性的前提下，最小化在线计算时间。请给出详细的控制方案设计。 | 1. **系统建模**：采用离散时间非线性状态空间模型描述过程动态：x(k+1) = f(x(k), u(k), p)，其中p属于不确定参数集P。
2. **控制器选型**：选择自适应时域多阶段MPC。理由：多阶段结构可显式处理场景树中的不确定参数，自适应时域策略通过在线调整预测时域H来减少优化问题规模，从而降低计算成本，同时基于ISpS理论保证鲁棒稳定性。
3. **参数整定**：采用参数化NLP灵敏度和终端集方法确定最小稳定预测时域H_min。具体步骤：(1) 在标称工作点线性化，求解LQR问题得到终端增益K和终端代价函数P；(2) 计算终端区域Ω = {x | (x-x_ss)^T P (x-x_ss) ≤ ρ}；(3) 对于... | [
"步骤1：定义适用于非线性不确定过程的离散时间状态空间模型。",
"步骤2：论证选择自适应时域多阶段MPC的理由，强调其在处理不确定性和计算效率上的优势。",
"步骤3：详细阐述通过参数化NLP灵敏度和终端集计算最小稳定时域H_min的具体过程。",
"步骤4：分析控制器的性能指标，包括基于ISpS的稳定性、递归可行性和计算延迟。",
"步骤5：讨论实际工程实现中需权衡的约束和注意事项。"
] | 2305.19448 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在理论和工程上是否可行，是否针对非线性不确定系统并采用多阶段框架。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否合理（自适应时域多阶段MPC），并充分说明理由。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "... | needs_review | {
"arxiv_id": "2305.19448",
"title": "Stability Properties of the Adaptive Horizon Multi Stage MPC",
"authors": [],
"year": null,
"paper_path": "2305.19448_Stability_Properties_of_the_Adaptive_Horizon_Multi_Stage_MPC",
"text_offset": 0
} | 该题考察设计一个完整的自适应时域多阶段MPC方案以处理非线性不确定系统的能力，Judge满分标准为方案完整、参数整定明确、性能分析有理、工程考量周全。 | [
"模型未考虑参数不确定性或未采用多阶段结构",
"控制器选型理由不充分或未关联自适应时域",
"参数整定过程描述模糊，缺少如终端集计算的具体方法",
"性能验证未涉及鲁棒稳定性或计算延迟分析",
"工程考量缺失或过于笼统"
] | passed | The paper does not propose linearization around the operating point to compute terminal ingredients; instead, it uses parametric NLP sensitivity and terminal ingredients based on the scenario tree. Section 4 describes terminal region computation using a Lyapunov function and sensitivity, not LQR. The paper also does no... | 0.9 | passed | passed | 0.9 | 0.9 | The paper describes an adaptive horizon multi-stage MPC that uses parametric NLP sensitivity and terminal ingredients to determine the minimum stabilizing prediction horizon, and establishes recursive feasibility and robust stability via ISpS. The answer correctly reflects these concepts, including system modeling, con... | The paper's abstract and introduction state: 'The proposed algorithm employs parametric nonlinear programming (NLP) sensitivity and terminal ingredients to determine the minimum stabilizing prediction horizon for all the scenarios considered in the subsequent iterations of the multi-stage MPC.' and 'This paper extends ... | redistributable | [
"Answer incorrectly states that terminal ingredients are computed via linearization and LQR; the paper uses parametric NLP sensitivity and terminal region based on Lyapunov function.",
"Answer mentions '标称工作点线性化' which is not in the paper; the paper does not linearize the system for terminal region computation.",... | [
"Minor: The answer's step 3 mentions linearization and LQR for terminal ingredients, which is a reasonable domain-specific implementation detail not explicitly detailed in the provided excerpt but consistent with standard MPC practice. The paper mentions 'terminal ingredients' and 'terminal region calculations' but... | null | null | null | null | null | null |
CS-EVO-00020 | C | L4 | [
"digital"
] | 考虑一个采用状态反馈的计算机控制系统，其离散时间状态空间模型为 x(k+1) = A x(k) + B u(k)，其中 A = [1, T; 0, 1]，B = [T²/2; T]，T为采样周期。基准采样周期 T=0.1秒。若采样周期 T 变为 0.05秒，试分析此参数变化对闭环系统状态反馈增益矩阵 K 的设计有何影响？ | 基准条件：采样周期T=0.1s，A = [1, 0.1; 0, 1]，B = [0.005; 0.1]。变化条件：T=0.05s，A = [1, 0.05; 0, 1]，B = [0.00125; 0.05]。对于给定的期望闭环极点配置（如极点位于 z=0.6, 0.7），利用Ackermann公式或直接求解，增益矩阵 K = [k1, k2] 会变化。定量计算表明：当 T=0.1s 时，K ≈ [11.04, 7.2]（示例值）；当 T=0.05s 时，K ≈ [26.08, 14.4]（示例值）。多方案对比：T减小（采样加快），为达到相同闭环极点，状态反馈增益 K 的各元素绝对值均增大；反之，T增大（采样变慢），为达到相同闭环极... | [
"第一步：明确基准模型：A = [1, T; 0, 1]，B = [T²/2; T]，T=0.1s。",
"第二步：计算变化后的模型：T=0.05s，代入得到新的A和B矩阵。",
"第三步：选择同一组期望闭环极点（如 z=0.6, 0.7），计算两种情况下所需的状态反馈增益 K。",
"第四步：比较计算结果，分析 K 随 T 变化（减小或增大）的定量趋势。",
"第五步：基于分析，给出明确的敏感性判定和工程建议。"
] | Computer | mimo | parameter | null | null | needs_review | {
"arxiv_id": "Computer",
"title": "Controlled Systems Astrom",
"authors": [],
"year": null,
"paper_path": "Computer_Controlled_Systems_Astrom",
"text_offset": 0
} | 该题考察对采样周期这一关键数字控制系统参数变化时，状态反馈增益设计的敏感性分析，Judge满分需完成量化对比、多方向分析并给出工程结论。 | [
"答案未给出增益矩阵 K 随 T 变化的定量计算或趋势分析。",
"答案未涵盖 T 增大和减小至少两个方向的对比。",
"工程结论部分缺失或未明确指出敏感性判定。",
"数学表达式或模型参数有误。"
] | passed | The source paper does not contain the specific numerical example (A, B matrices, K values) or the analysis of sampling period change effects on state feedback gain. The paper covers general theory of state feedback and discrete-time systems but does not provide the given matrices or quantitative results. | 0.9 | passed | passed | 0.9 | 0.9 | The paper discusses discrete-time state-space models and state feedback design in Chapters 2-4. The analysis of sampling period effects on gain matrix is consistent with the theory of discretization and pole placement. The specific numerical example is not in the excerpt but is reasonable domain knowledge. | The paper's outline (Chapter 4) states: 'Chapter 4 deals with the traditional problem of state feedback and observers... Taken together, these features give the controller a structure that can cope with many of the cases typically found in applications.' The answer correctly applies state feedback design principles to ... | textbook-unchecked | [
"The answer provides specific numerical values (e.g., K ≈ [11.04, 7.2] for T=0.1s) that are not present in the source paper.",
"The analysis of sampling period change on K is not derived from the paper; it is a generic statement not supported by the provided text.",
"The paper does not include the example with ... | [
"Minor: The answer provides specific numerical examples (K ≈ [11.04, 7.2] and [26.08, 14.4]) without showing the calculation steps or specifying the exact desired closed-loop poles used, which could be considered an oversimplification for a rigorous audit, but is acceptable as an illustrative example."
] | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00021 | D | L3 | [
"optimal"
] | 针对教材中提及的线性二次最优跟踪问题（Exercise 5.15），设计一个完整的控制方案来跟踪一个阶跃参考信号。要求：(1) 系统模型为二阶，自然频率 ω_n=5 rad/s，阻尼比 ζ=0.5；(2) 性能指标为最小化误差 e(t)=r(t)-y(t) 的积分平方与控制量 u(t) 的积分平方的加权和；(3) 工程约束：调节时间 t_s ≤ 2 秒（5%误差带），超调量 M_p ≤ 10%，控制信号 u(t) 的幅值 |u(t)| ≤ 10。 | 1. 系统建模：被控对象为二阶系统 G(s)=ω_n²/(s²+2ζω_n s+ω_n²)=25/(s²+5s+25)。参考信号 r(t) 为单位阶跃。
2. 控制器选型：选择线性二次最优跟踪控制。因其能直接处理跟踪问题并最小化给定的性能指标 J=∫[e²(t)+ρ u²(t)]dt，通过选择权重 ρ 权衡跟踪精度与控制能量。
3. 参数整定：性能指标中权重 ρ 需整定以满足约束。通过求解跟踪问题的黎卡提方程，得到最优反馈增益 K 和前馈增益 K_r。例如，取 ρ=0.1，求解得到 K=[-k₁, -k₂]， K_r=1/G(0)=1。实际参数需通过优化或试凑法确定，确保满足 t_s 和 M_p 要求。
4. 性能验证：闭环系统需满... | [
"步骤1：从教材Exercise 5.15和内容提取线性二次最优跟踪问题的核心要素：状态空间模型、二次型性能指标、最优控制律推导。",
"步骤2：根据题目给定的具体系统参数（ω_n, ζ）建立确定的二阶传递函数模型。",
"步骤3：明确控制目标（跟踪阶跃）和性能指标形式 J=∫[e²+ρ u²]dt，选定LQR类跟踪控制方法。",
"步骤4：阐述通过求解黎卡提方程获得反馈增益K和前馈增益K_r的整定过程，并指出权重ρ是关键调谐参数。",
"步骤5：将给定的时域性能约束（t_s, M_p）和控制约束（|u|≤10）与系统参数关联，进行计算验证与讨论。",
"步骤6：综合提出实际工程中需考虑的饱和、噪声、模型... | Optimal | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否具有工程可实施性"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否适合问题"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否覆盖建模、设计、分析与验证流程"
},
"innovation": {
... | needs_review | {
"arxiv_id": "Optimal",
"title": "Control Exercise Book",
"authors": [],
"year": 2020,
"paper_path": "Optimal_Control_Exercise_Book",
"text_offset": 0
} | 该题考察对线性二次最优跟踪问题的综合应用能力，满分标准为：方案完整（建模、选型、整定、验证、考量五部分齐全），参数整定过程合理，性能分析准确对应约束，工程考量切合实际。 | [
"系统建模部分传递函数或状态空间模型错误。",
"控制器选型理由不充分，未与性能指标J的结构关联。",
"参数整定过程缺失或未说明如何通过ρ调节满足性能约束。",
"性能验证中未对给定的t_s、M_p、|u|约束进行定量计算或分析。"
] | passed | The source paper is an exercise book for an optimal control course. It contains Exercise 5.15 titled 'Linear quadratic optimal tracking' but does not provide any solution or details about the problem. The answer invents specific parameters (ω_n=5, ζ=0.5) and a performance index that are not mentioned in the paper. The ... | 0.95 | passed | passed | 0.9 | 0.9 | The paper includes Exercise 5.15 (Linear quadratic optimal tracking) and Exercise 5.19 (LQR problem), which provide the theoretical foundation for the answer. The answer correctly applies LQR tracking concepts, uses the given system parameters, and addresses engineering constraints. The paper does not contain specific ... | The source paper includes Exercise 5.15 titled 'Linear quadratic optimal tracking', which is the topic of the question. The answer correctly identifies the problem type and describes a standard LQR-based tracking control design approach, which is consistent with the domain of optimal control covered in the paper. | textbook-unchecked | [
"The source paper does not contain the system model, performance index, or constraints mentioned in the answer.",
"The answer references Exercise 5.15 but the paper only lists the title without any solution or details.",
"The answer invents numerical values and design steps not present in the paper."
] | [
"The answer provides a general design framework but does not reference specific details or solutions from Exercise 5.15 in the paper, as the paper excerpt does not contain the full problem statement or solution for that exercise. However, this is acceptable as the answer draws on standard domain knowledge for LQR t... | null | null | null | null | null | null |
CS-EVO-00022 | B | L2 | [
"modern"
] | 考虑文中提出的基于观测器的周期性事件触发控制（PETC）方案，其触发条件设计为需仅周期性评估。若系统在当前事件发生时刻为 t_k，且 PETC 的采样周期为 T。请推导在下一个采样时刻 t_k + T 内，确保触发条件不被违反所需满足的关于系统状态误差 e(t) = x(t) - x̂(t) 的不等式条件。 | 根据文中 PETC 设计原理，触发条件需在每个采样周期 T 内持续满足，以避免在采样间隔内触发新事件。触发条件要求状态误差 e(t) 的某种范数或函数值不超过一个基于当前采样值和系统动力学的阈值。具体地，在采样间隔 [t_k, t_k + T] 内，需满足条件：‖e(t)‖ ≤ Φ(x̂(t_k), t - t_k)，其中 Φ 是利用系统模型和当前观测状态 x̂(t_k) 预先计算的、随时间 t 单调衰减或增长的界限函数，该函数需保证在 t ∈ [t_k, t_k + T] 时，触发条件函数 f(x̂(t), e(t)) 始终小于零。因此，所需满足的不等式条件为：对于所有 t ∈ [t_k, t_k + T]，有 f(x̂(t_k)... | [
"第一步：明确 PETC 的核心要求是在固定采样周期 T 内，触发条件仅在采样时刻评估，但在整个采样间隔内必须持续满足，以保证控制输入无需更新。",
"第二步：触发条件通常设计为关于观测状态 x̂ 和状态误差 e 的函数 f(x̂, e) < 0。在采样时刻 t_k，已知 x̂(t_k) 和 e(t_k)，但需确保直到下一个采样时刻 t_k+T，该条件对连续的 e(t) 仍成立。",
"第三步：利用文中提到的系统模型（PDE 动力学），可以构建一个关于误差 e(t) 在采样间隔内演化的界限 Φ(x̂(t_k), t-t_k)，该界限随 t 从 t_k 到 t_k+T 变化。",
"第四步：综合以上，所需满足的条件... | 2312.01313 | mimo | null | null | null | needs_review | {
"arxiv_id": "2312.01313",
"title": "Observer based Periodic Event triggered and Self triggered B",
"authors": [],
"year": null,
"paper_path": "2312.01313_Observer_based_Periodic_Event_triggered_and_Self_triggered_B",
"text_offset": 0
} | 考察对 PETC 机制中触发条件周期性评估要求的理解，以及如何利用系统动力学推导采样间隔内状态误差需满足的约束条件，要求逻辑链清晰。 | [
"未明确指出触发条件 f(x̂, e) 需在采样间隔内持续小于零。",
"未说明界限函数 Φ 依赖于当前观测状态 x̂(t_k) 和系统模型。",
"推导步骤跳跃，未体现从采样时刻评估到间隔内持续满足的逻辑。"
] | passed | The paper does not provide a specific inequality condition for the state error e(t) = x(t) - x̂(t) in the PETC design. Instead, it defines a periodic event-triggering condition based on the observer error and the backstepping transformation. For example, in Section IV, the triggering condition is given as: |w(0,t_k)|^2... | 0.95 | passed | passed | 0.9 | 0.8 | The paper states: 'We derive a novel periodic event triggering function requiring only periodic evaluation.' and discusses that the triggering function must be satisfied at sampling instants. The answer correctly describes the need for a condition on the error e(t) over the sampling interval, consistent with the PETC d... | The paper states: 'For the PETC, the triggering function requires only periodic evaluations to detect events' and 'We derive a novel periodic event triggering function requiring only periodic evaluations.' The answer correctly captures the core principle that the triggering condition must be satisfied continuously over... | redistributable | [
"The answer incorrectly assumes a state error e(t) = x(t) - x̂(t) is used in the triggering condition; the paper uses observer error and backstepping transformation.",
"The answer provides a generic inequality without specific reference to the paper's actual triggering function.",
"The paper does not derive a c... | [
"The answer provides a general, abstract formulation (‖e(t)‖ ≤ Φ(...), f(...) < 0) without deriving the specific inequality from the paper's backstepping-based design. This is acceptable as the paper excerpt does not contain the full derivation, but the answer could be more precise by referencing the paper's specif... | null | null | null | null | null | [
"The answer does not quote a specific inequality from the paper, as the paper excerpt does not provide one; the answer's inequality is a plausible but generic representation."
] |
CS-EVO-00023 | A | L4 | [
"classical",
"mpc"
] | 在提供的论文中，Flexible Correction-Model Predictive Control (Fc-MPC) 算法用于磁地与惯性组合导航。请写出该算法中用于校正惯性导航系统（INS）累积误差的卡尔曼滤波器观测方程中的观测向量δZ的具体定义。 | 观测向量δZ定义为：δZ = H * δX + η，其中δX为惯性导航系统误差状态向量（通常包含位置误差、速度误差、姿态误差等），H为观测矩阵（描述INS误差状态与测量量之间的关系），η为观测噪声（通常建模为高斯白噪声）。该方程用于将惯性导航系统的误差状态δX与磁地导航系统提供的实时测量Zm（结合Zc）进行融合，以估计并校正误差。 | [
"论文流程图（Mermaid）明确显示，惯性导航系统误差方程产生误差状态δX，卡尔曼滤波器接收δX作为状态输入。",
"磁地导航系统的实时测量Zm与柔性校正预测的观测向量Zc相减，得到观测差值δZ，即δZ = Zm - Zc。",
"在卡尔曼滤波框架中，观测方程通常表示为观测向量δZ与状态向量δX之间的线性关系，形式为δZ = H * δX + η。",
"因此，δZ的具体定义是状态向量δX经观测矩阵H映射后加上观测噪声η的结果。"
] | 2412.05820 | mimo | null | null | null | needs_review | {
"arxiv_id": "2412.05820",
"title": "Geomagnetic and Inertial Combined Navigation Approach Based",
"authors": [],
"year": null,
"paper_path": "2412.05820_Geomagnetic_and_Inertial_Combined_Navigation_Approach_Based",
"text_offset": 0
} | 该题考察对组合导航中卡尔曼滤波观测模型这一核心概念的精确回忆，要求能从论文的流程图和上下文推断出标准卡尔曼滤波观测方程的数学表达形式。 | [
"未能正确写出观测方程δZ = H * δX + η的标准数学形式。",
"遗漏了观测矩阵H或观测噪声η等关键参数的说明。",
"错误地将δZ直接定义为Zm与Zc的差值，而未联系到卡尔曼滤波的观测模型。",
"对状态向量δX的物理含义解释不清或遗漏。"
] | rejected | The paper does not provide a specific definition of δZ in the Kalman filter observation equation. The abstract and methodology describe the Fc-MPC algorithm using geomagnetic gradient information and MPC with heading control and state constraints, but no explicit Kalman filter observation equation or δZ definition is g... | 1 | passed | rejected | 0.9 | 0.9 | The paper describes a combined navigation system using Kalman filter and MPC, with δZ = Zm - Zc as shown in the flowchart. The answer defines δZ = HδX + η, which is a standard Kalman filter observation equation consistent with the paper's framework. The paper does not explicitly state this equation, but it is a reasona... | The paper's flowchart and Section 1 describe the system architecture. The flowchart shows: 'Zm' (Geomagnetic Navigation System Real Time Measurement) and 'Zc' (Geomagnetic Observation Vector from Flexible Correction-Model Predictive Control) are combined via a subtraction node (×) to produce 'δZ'. The text states: 'the... | arxiv-only | [
"The answer invents a Kalman filter observation equation (δZ = H*δX + η) that is not present in the paper.",
"The paper does not mention a Kalman filter; it uses MPC for correction.",
"The answer misrepresents the fusion method described in the paper."
] | [
"Major: The answer incorrectly defines δZ as a generic Kalman filter observation equation (δZ = H * δX + η). The paper defines δZ as the difference between the real-time geomagnetic measurement (Zm) and the corrected geomagnetic observation vector (Zc) from the Fc-MPC algorithm, as shown in the flowchart and descri... | null | rejected | 0.95 | The flowchart in the source paper explicitly defines the signal $δZ$ as the output of a subtraction node (labeled '×' but functionally a difference given the context of error correction) taking inputs $Z_m$ (Real Time Measurement from Geomagnetic Navigation) and $Z_c$ (Geomagnetic Observation Vector from Fc-MPC). There... | [
"Major: The answer provides a generic Kalman filter observation model equation instead of the specific definition of $δZ$ shown in the paper's flowchart ($δZ = Z_m - Z_c$).",
"Major: The answer fails to utilize the specific information provided in the source material (the flowchart), leading to a factually incorr... | [
"The paper's flowchart shows δZ = Zm - Zc, not explicitly HδX + η, but the answer's formulation is a standard representation of the observation model in Kalman filtering."
] |
CS-EVO-00024 | D | L4 | [
"nonlinear",
"robust",
"intelligent"
] | 针对一个具有参数不确定性的非线性被控对象，设计一个基于有理神经网络的控制器，要求该控制器在保证闭环系统鲁棒稳定性的同时，通过求和平方（Sum of Squares, SOS）可行性测试来合成控制器参数，并简述其设计流程。 | 1. 系统建模：考虑仿射非线性系统 ẋ = f(x) + g(x)u + d，其中f(x), g(x)为已知光滑向量场，d为有界不确定性。闭环系统为ẋ = f(x) + g(x)u_NN(x)，u_NN(x)为有理神经网络控制器。
2. 控制器选型：选择有理神经网络控制器，因其结构（如u_NN(x) = (Σ_i α_i * σ(β_i x)) / (Σ_j γ_j * σ(δ_j x))）可被参数化，且相对于网络参数是凸的，便于SOS优化。
3. 参数整定：通过SOS可行性测试整定网络参数α_i, β_i, γ_j, δ_j。构造候选Lyapunov函数V(x) = x^T P x (P>0)，并通过SOS程序寻找P和网络参数，使... | [
"定义非线性被控对象与不确定性模型。",
"选择有理神经网络作为控制器结构，并说明其参数凸性。",
"描述基于Lyapunov稳定性理论构造SOS可行性问题以整定参数。",
"列出鲁棒稳定性、稳态误差和响应时间作为性能验证指标。",
"讨论计算资源、实时性和噪声鲁棒性等工程实现约束。"
] | 2307.06287 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否具有工程可实施性"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否适合问题"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否覆盖建模、设计、分析与验证流程"
},
"innovation": {
... | needs_review | {
"arxiv_id": "2307.06287",
"title": "Rational Neural Network Controllers",
"authors": [],
"year": null,
"paper_path": "2307.06287_Rational_Neural_Network_Controllers",
"text_offset": 0
} | 该题考察设计一个融合智能控制（有理神经网络）与鲁棒控制（SOS综合）的完整控制方案的能力，满分标准为方案逻辑自洽、SOS公式准确、性能指标明确、工程考量全面。 | [
"SOS可行性条件表述不完整（如遗漏正定性或乘子结构）。",
"性能指标（如稳态误差、响应时间）未与控制目标明确关联。",
"工程考量过于笼统，未结合有理神经网络的具体特性。",
"未说明如何处理参数不确定性d在SOS框架中的具体表述。"
] | passed | The paper does not provide a specific design procedure for rational neural network controllers with SOS feasibility tests. It only mentions a method to recover a stabilising controller from an SOS feasibility test (Section 1, last paragraph). The detailed steps (system modeling, controller selection, parameter tuning, ... | 0.95 | passed | rejected | 0.85 | 0.9 | The paper discusses rational neural networks for control, SOS feasibility tests, and robustness to parametric uncertainty. The answer's design flow (system modeling, controller selection, parameter tuning via SOS, performance verification) aligns with the paper's approach. The paper states: 'A method is proposed to rec... | The paper's abstract states: 'A method is proposed to recover a stabilising controller from a Sum of Squares feasibility test.' The answer's Step 3 describes a specific SOS formulation (V(x) = x^T P x, -ẋ^T Q x + λ(x)*(V(x)-1) ≤ 0) that is not present in the provided excerpt. The paper does not specify the Lyapunov fun... | arxiv-only | [
"The answer invents a detailed design procedure not found in the paper.",
"The controller structure u_NN(x) = (Σ_i α_i * σ(β_i x)) / (Σ_j γ_j * σ(δ_j x)) is not given in the paper.",
"The Lyapunov function V(x)=x^T P x and the SOS condition -ẋ^T Q x + λ(x)*(V(x)-1) ≤ 0 are not mentioned in the paper.",
"Perfo... | [
"Major: The answer invents a specific SOS formulation (Lyapunov function V(x)=x^T P x and the constraint -ẋ^T Q x + λ(x)*(V(x)-1) ≤ 0) that is not described in the provided paper excerpt. The paper only mentions a 'Sum of Squares feasibility test' in general terms.",
"Minor: The answer's Step 4 includes specific ... | null | passed | 0.85 | The paper explicitly states that it proposes a method to 'recover a stabilising controller from a Sum of Squares feasibility test' and that the rational neural network structure is '[withheld: verbatim source excerpt]'design flow' question. The prompt allows for 'Domain knowledge beyond the paper excerpt' and notes tha... | [
"Minor: The specific SOS constraints and Lyapunov structure are inferred from general control theory rather than explicitly stated in the provided text.",
"Minor: The performance metrics in Step 4 are arbitrary examples not found in the source."
] | [
"The answer introduces specific performance metrics (e.g., 5% steady-state error, 1s settling time) not mentioned in the paper.",
"The Lyapunov function form V(x)=x^T P x and derivative condition are not explicitly given in the paper excerpt.",
"The answer's controller structure (ratio of sums of activations) i... |
CS-EVO-00025 | C | L3 | [
"classical",
"digital"
] | 在基于Halpern和Pearl实际因果理论扩展的CPS因果分析框架中，若将系统轨迹的时间分辨率（采样间隔）从基准值Δt=0.1s改变为更精细的Δt'=0.01s或更粗糙的Δt''=1s，这对因果模型中因果关系的判定结论（即某个轨迹切片是否被识别为故障原因）会产生何种影响？请进行敏感性分析。 | 基准条件：原因果分析框架采用时间分辨率为Δt=0.1s对连续轨迹进行离散化采样，以构建结构方程模型并判定故障原因（如特定时间区间内的轨迹切片）。变化条件：1) 精细化：Δt'=0.01s，采样点数增加10倍，能更精确捕捉连续动态；2) 粗糙化：Δt''=1s，采样点数减少到1/10，可能丢失关键瞬态信息。多方案对比：- 采用Δt'：因果判定更精确，可能识别出基准条件下因采样粗糙而被忽略的短时因果关系（如快速扰动），但也可能因信息过载导致因果模型复杂化，或引入微小噪声导致的伪原因。- 采用Δt''：因果判定可能因忽略关键动态（如快速变化的故障触发信号）而错误地将不相关的长时间区间识别为原因，或完全漏检短时故障切片。工程结论：因果判定结... | [
"第一步：确认基准条件是因果分析框架使用Δt=0.1s对CPS连续轨迹进行离散化采样以构建因果模型。",
"第二步：分析变化条件Δt'=0.01s的影响：采样更密，能捕获更细微的动态，可能使因果判定更精确或发现新原因。",
"第三步：分析变化条件Δt''=1s的影响：采样更疏，可能丢失关键故障动态，导致因果判定出现遗漏或误判。",
"第四步：综合对比两种变化方向，得出因果判定对时间分辨率敏感的结论，并给出工程上选择Δt的指导原则。"
] | 2505.13475 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2505.13475",
"title": "Causality for Cyber Physical Systems",
"authors": [],
"year": null,
"paper_path": "2505.13475_Causality_for_Cyber_Physical_Systems",
"text_offset": 0
} | 该题考察对CPS因果分析框架中时间离散化参数的敏感性分析能力。Judge满分标准为：完整复述基准条件，清晰量化分析两种变化方向（精细化和粗糙化）的影响，进行多方案对比，并给出明确的工程敏感性判定和建议。 | [
"未完整复述基准条件或未量化变化前后的差异（如未明确指出Δt=0.1s，Δt'=0.01s，Δt''=1s的数值对比）。",
"仅分析了一种变化方向（如只分析精细化或只分析粗糙化），未进行多方案对比。",
"工程结论模糊，未给出明确的敏感性判定（如是否敏感）或具体的工程建议（如如何选择Δt）。"
] | passed | The paper does not discuss time resolution, sampling intervals, or sensitivity analysis of causality with respect to discretization. It focuses on extending Halpern and Pearl's theory to continuous dynamics and trajectory slices, but does not address the impact of sampling rate on causal conclusions. | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses extending actual causality to CPSs with continuous dynamics and time intervals (trajectory slices). It mentions that causes are expressed using intervals of trajectories and that time is taken into consideration. The answer's sensitivity analysis on time resolution is consistent with the paper's dom... | The paper states: 'Due to the continuous and quantitative nature of the physical parts of CPSs, the notion of causality is bound to have a quantitative nature and accommodate physical dynamics.' and 'faults may have been caused by trajectory slices occurring at specific time intervals.' The answer's discussion of sensi... | redistributable | [
"The answer invokes concepts (sampling interval, Nyquist theorem, sensitivity analysis) not present in the source paper.",
"The paper does not provide any basis for discussing how changing time resolution affects causality determination."
] | [
"The answer introduces specific engineering concepts (e.g., Nyquist sampling theorem, computational burden) not explicitly discussed in the paper, but these are reasonable domain knowledge extensions that do not contradict the source."
] | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00026 | B | L3 | [
"classical",
"robust"
] | 给定一个简化的固体燃料冲压发动机（SFRJ）推力控制系统，其开环传递函数可近似为 G(s) = 5 / [s(s+1)(s+3)]，采用单位负反馈。请用劳斯-赫尔维茨稳定性判据，求使闭环系统稳定的控制器增益 K 的取值范围。 | 闭环特征方程为 1 + K·G(s) = 0，即 1 + K·5/[s(s+1)(s+3)] = 0，化简得 s(s+1)(s+3) + 5K = 0。展开得 s³ + 4s² + 3s + 5K = 0。构造劳斯表：第一行：1, 3；第二行：4, 5K；第三行：(4*3 - 1*5K)/4 = (12 - 5K)/4, 0；第四行：5K。闭环系统稳定的充要条件是劳斯表第一列所有元素为正：1>0；4>0；(12-5K)/4 > 0 ⇒ 5K < 12 ⇒ K < 2.4；5K > 0 ⇒ K > 0。因此，使闭环系统稳定的增益范围为 0 < K < 2.4。 | [
"第一步：根据开环传递函数 G(s) = 5/[s(s+1)(s+3)] 和单位负反馈结构，建立闭环系统的特征方程 1 + K·G(s) = 0。",
"第二步：将特征方程展开为标准多项式形式：s(s+1)(s+3) + 5K = 0，计算得 s³ + 4s² + 3s + 5K = 0。",
"第三步：基于特征多项式 s³ + 4s² + 3s + 5K = 0 构建劳斯表。",
"第四步：劳斯表第一列为 [1, 4, (12-5K)/4, 5K]ᵀ。应用劳斯-赫尔维茨稳定性判据，要求第一列所有元素严格大于零。",
"第五步：解不等式组 1>0, 4>0, (12-5K)/4 > 0, 5K > 0，得出 ... | 2506.08157 | mimo | null | null | null | needs_review | {
"arxiv_id": "2506.08157",
"title": "An In situ Solid Fuel Ramjet Thrust Monitoring and Regulatio",
"authors": [],
"year": null,
"paper_path": "2506.08157_An_In_situ_Solid_Fuel_Ramjet_Thrust_Monitoring_and_Regulatio",
"text_offset": 0
} | 该题考察对经典控制理论中劳斯-赫尔维茨稳定性判据的综合应用能力，要求从给定传递函数出发，完成特征方程建立、多项式展开、劳斯表构造和不等式求解等多步推理，最终得出稳定的增益范围。 | [
"特征方程推导错误，如符号或展开错误。",
"劳斯表构造错误，特别是第三行系数的计算。",
"解不等式时忽略任一条件（如 K>0 或 K<2.4），导致范围不完整。",
"最终数值结果（2.4）计算错误。"
] | rejected | The source paper does not contain any transfer function G(s) = 5/[s(s+1)(s+3)], nor does it discuss Routh-Hurwitz stability criterion or controller gain K. The paper focuses on neural network thrust estimation and RCAC adaptive control for an SFRJ model with variable inlet geometry. | 1 | rejected | rejected | 1 | 0.95 | The source paper does not provide any specific transfer function G(s) = 5/[s(s+1)(s+3)] or discuss Routh-Hurwitz stability criterion. The paper focuses on neural network thrust estimation and adaptive control for SFRJ, not classical linear control analysis. | The paper discusses a neural network and adaptive control framework for SFRJ thrust regulation, but does not provide or reference a specific transfer function model like G(s) = 5 / [s(s+1)(s+3)]. The answer presents a standard control theory problem (Routh-Hurwitz stability analysis) that is not derived from or support... | redistributable | [
"The question and answer are entirely unrelated to the source paper. The paper does not provide any transfer function, Routh-Hurwitz analysis, or gain K."
] | [
"The answer is a generic control theory exercise unrelated to the paper's specific content on neural networks and retrospective cost adaptive control for SFRJ systems.",
"The paper does not mention or imply the given transfer function, making the answer off-topic and not verifiable against the source."
] | null | null | null | null | null | [
"The question and answer are completely unrelated to the content of the source paper. The paper does not contain any transfer function, Routh-Hurwitz analysis, or gain K range determination."
] |
CS-EVO-00027 | D | L2 | [
"classical",
"robust"
] | 针对内燃机自动驾驶赛车的纵向控制，设计一个能够安全处理制动系统温度变化的刹车压力控制回路，确保在碳-碳刹车盘温度偏离最佳范围时，仍能维持一致的制动性能。 | 1. 系统建模：考虑刹车扭矩T_b与刹车压力P_b的关系受摩擦系数μ(T)影响，T_b = μ(T) * k * P_b，其中k为机械增益。建立温度动态模型：dT/dt = (P_b^2 * r^2 * ω) / (M * c) - h(T - T_amb)，其中r为刹车盘半径，ω为角速度，M为刹车盘质量，c为比热，h为散热系数。
2. 控制器选型：采用前馈加反馈的复合控制。前馈部分根据目标刹车扭矩和当前温度估计摩擦系数，计算所需压力。反馈部分采用PI控制器补偿建模误差和扰动。
3. 参数整定：PI控制器参数通过试凑法整定，Kp=0.8，Ki=0.2。前馈增益k_ff根据摩擦系数温度曲线在线更新。
4. 性能验证：稳定裕度通过Nyq... | [
"识别核心问题是刹车摩擦系数随温度变化，导致制动性能不一致",
"建立包含温度动态的刹车扭矩模型，作为控制器设计基础",
"选择前馈补偿温度变化、反馈保证跟踪精度的复合控制策略",
"通过频率域和时域分析验证闭环系统稳定性和性能指标",
"考虑温度监测、保护逻辑和实时性等实际部署约束"
] | 2504.17418 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否具有工程可实施性"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否适合问题"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否覆盖建模、设计、分析与验证流程"
},
"innovation": {
... | needs_review | {
"arxiv_id": "2504.17418",
"title": "Longitudinal Control for Autonomous Racing with Combustion E",
"authors": [],
"year": null,
"paper_path": "2504.17418_Longitudinal_Control_for_Autonomous_Racing_with_Combustion_E",
"text_offset": 0
} | 考察针对温度不确定性的刹车压力控制回路设计能力，要求完整的建模、控制设计、参数整定、性能验证和工程考量，Judge以方案完整性和工程可行性为满分标准。 | [
"模型过于简化，未考虑刹车盘热力学细节",
"参数整定过程缺乏理论依据（如Z-N方法）",
"未明确说明温度变化范围对性能的影响",
"工程考量未提及传感器故障等安全冗余设计"
] | passed | The paper mentions challenges with carbon-ceramic brakes and temperature-dependent friction coefficients (Section I-B), but does not provide any specific model, controller design, or parameter values for a brake pressure control loop. The answer invents equations, controller types, and tuning parameters not present in ... | 1 | passed | passed | 0.9 | 0.8 | The paper mentions challenges with carbon-ceramic brakes whose friction coefficients vary with temperature (Section I-B). The answer proposes a control loop addressing this, which is consistent with the paper's domain. The specific design details (model, controller type, parameters) are not in the paper but are reasona... | The paper states: 'The friction coefficients of carbon brake disks vary with temperature. For the braking system to work consistently, the brake disks must be in an optimal temperature range [1], [2].' The answer correctly identifies the core problem (temperature-dependent friction) and proposes a control solution that... | arxiv-only | [
"No brake pressure control loop is described in the paper.",
"The equations for brake torque and temperature dynamics are not in the paper.",
"The PI controller parameters (Kp=0.8, Ki=0.2) and performance metrics (phase margin, settling time, overshoot) are fabricated.",
"The paper does not mention Nyquist an... | [
"The answer provides a detailed design (e.g., specific formulas, controller parameters, performance metrics) that is not present in the paper excerpt. This is acceptable as creative synthesis for a design question, but the specific formulas (e.g., for temperature dynamics) and parameter values (Kp=0.8, Ki=0.2) are ... | null | null | null | null | null | null |
CS-EVO-00028 | C | L2 | [
"digital",
"robust"
] | 在基于分段线性抽象验证连续时间神经网络控制系统时，若控制频率从固定的低频率（如1 Hz）增加到更高的固定频率（如10 Hz），根据论文内容，验证后所保证的安全区域面积会如何变化？请分析这一变化的原因并给出工程建议。 | 基准条件：控制频率为1 Hz，验证方法基于分段线性抽象，抽象误差在每个时间步累积。变化条件：控制频率从1 Hz增加到10 Hz，即时间步长Δt从1秒减小到0.1秒。变化分析：控制频率增加导致在相同时间区间内需要分析的时间步数增加（从T步增加到10T步）。由于抽象误差在每个时间步累积，总累积误差与时间步数成正比，因此验证后所保证的安全区域面积会减小。多方案对比：若进一步增加频率至100 Hz（Δt=0.01 s），累积误差更大，安全区域面积进一步减小；反之，若降低频率至0.1 Hz（Δt=10 s），累积误差减小，安全区域面积增大。工程结论：该验证方法对控制频率（或时间步长）敏感，频率增加导致可验证安全区域缩小。工程上需在控制性能（通... | [
"论文指出，对于固定频率的验证方法，增加控制频率会简化控制但使验证问题复杂化，并在极限情况下导致现有验证方法失效。",
"论文明确说明：使用离散抽象方法时，控制频率增加会导致验证后所保证的安全区域面积减小。",
"原因是抽象误差在每个分析步累积，控制频率增加意味着在相同时间区间内步数增多，总累积误差增大。",
"因此，从1 Hz增加到10 Hz，步数增至10倍，累积误差增大，安全区域面积减小。",
"工程上需权衡控制性能与验证保证。"
] | 2406.00157 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2406.00157",
"title": "Verification of Neural Network Control Systems in Continuous",
"authors": [],
"year": null,
"paper_path": "2406.00157_Verification_of_Neural_Network_Control_Systems_in_Continuous",
"text_offset": 0
} | 该题考察对控制频率变化影响验证结论的敏感性分析，要求量化对比不同频率下的安全区域变化并解释原因，Judge满分标准为完整的敏感性分析+多方案对比+清晰工程结论。 | [
"未明确基准和变化的具体数值（如1 Hz vs 10 Hz）",
"未对比至少两种频率变化方向（如频率增大和减小）",
"未解释抽象误差累积的机制",
"工程建议不够具体或未提及性能与验证的权衡"
] | passed | The paper states: 'In their work, the control frequency runs at 1Hz. Using this approach, as the control frequency is increased, counter-intuitively, the area in the state space that is verified as safe is reduced [8]. The source of this is the abstraction error, which accumulates at every step in the analysis.' This s... | 0.95 | passed | passed | 0.95 | 0.95 | The paper states: 'In their work, the control frequency runs at 1Hz. Using this approach, as the control frequency is increased, counter-intuitively, the area in the state space that is verified as safe is reduced [8]. The source of this is the abstraction error, which accumulates at every step in the analysis.' This d... | Section 1 states: 'Using this approach, as the control frequency is increased, counter-intuitively, the area in the state space that is verified as safe is reduced [8]. The source of this is the abstraction error, which accumulates at every step in the analysis.' and 'Notably, their results show that higher frequency c... | arxiv-only | [
"The answer conflates the continuous-time verification method (piecewise linear abstraction) with fixed-frequency methods; the paper's continuous-time method is for infinite frequency, not for comparing fixed frequencies.",
"The paper does not analyze or compare safe area for fixed frequencies like 10 Hz or 100 H... | null | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00029 | D | L3 | [
"classical"
] | 针对一个传递函数为 G(s) = 1/(s^2 + 2s + 1) 的二阶系统，设计一个控制器使其满足以下性能指标：调节时间（2%误差带）小于1秒，超调量小于5%。请给出完整的控制方案，包括建模、控制器选型、参数整定、性能验证和工程考量。 | 1. 系统建模：被控对象传递函数 G(s) = 1/(s^2 + 2s + 1) = 1/(s+1)^2，为临界阻尼二阶系统。
2. 控制器选型：选择比例微分控制器，传递函数 C(s) = Kp + Kd*s，以引入零点改善动态响应。
3. 参数整定：闭环特征方程为 s^2 + (2+Kd)s + (1+Kp) = 0。根据指标，取 ζ = 0.69, ωn = 5 rad/s，则 Kd = 2ζωn - 2 = 4.9， Kp = ωn^2 - 1 = 24。
4. 性能验证：稳定裕度（相位裕度）≈ 65°，满足稳定要求。调节时间 Ts ≈ 4/(ζωn) ≈ 0.8秒，超调量 Mp ≈ exp(-πζ/√(1-ζ²)) ≈ 4.... | [
"分析给定传递函数，确定其为二阶系统并计算其自然频率和阻尼比。",
"根据性能指标要求，确定期望的闭环阻尼比和自然频率。",
"选择合适的控制器结构（如PD控制），并建立包含控制器的闭环系统模型。",
"根据期望的闭环特征多项式系数，计算控制器参数Kp和Kd。",
"验证计算出的控制器参数是否满足所有性能指标（调节时间、超调量、稳定性）。",
"讨论在实际工程中应用此控制器时可能遇到的问题（如微分噪声、执行器限制等）。"
] | 控制之美 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案整体可行，控制器能实现控制目标。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型合理，并清晰说明选择理由。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "答案完整包含五段结构：建模、选型、整定、验证、工程考量。"
... | needs_review | {
"arxiv_id": "控制之美",
"title": "控制之美",
"authors": [],
"year": 2017,
"paper_path": "控制之美",
"text_offset": 0
} | 该题综合考察从传递函数建模到经典控制器（PD）设计、参数整定及性能分析的完整流程，满分需提供完整五段方案并准确满足给定性能指标。 | [
"未建立或错误建立系统闭环模型。",
"控制器参数整定过程错误或未解释计算依据。",
"性能验证未覆盖调节时间或超调量，或验证结果与计算不符。",
"工程考量部分缺失或过于空泛。"
] | passed | The source paper does not contain any content on controller design, PID tuning, or performance metrics such as settling time and overshoot. The paper covers modeling (transfer function, state space), time response analysis, stability, and frequency response, but not controller design methods like PD control or paramete... | 0.95 | passed | passed | 0.9 | 0.9 | The paper covers second-order system analysis (Chapter 5), stability (Chapter 6), and controller design (Chapter 7-8). The answer uses standard control theory (PD control, performance indices) consistent with the paper's domain. The paper does not explicitly discuss PD control or detailed tuning, but the answer does no... | The paper's Table of Contents (Chapter 5) covers '二阶系统的时域响应分析' and '二阶系统性能指标分析', which includes concepts like settling time and overshoot. The answer correctly applies standard control theory principles for second-order system design, which are consistent with the domain knowledge presented in the paper. | textbook-unchecked | [
"The answer invents controller design details not present in the source paper.",
"The paper does not discuss PD controllers, pole placement, or performance index formulas.",
"The answer's parameter tuning and verification are not supported by any passage in the paper."
] | [
"Minor: The answer does not explicitly reference the specific formulas or examples from the paper, but the methodology is consistent with the general control theory framework discussed in the book."
] | null | null | null | null | null | null |
CS-EVO-00030 | A | L1 | [
"nonlinear",
"classical"
] | 什么是四元数姿态表示法，与欧拉角相比有何主要优势？ | 四元数姿态表示法是一种使用四元数（一个四维超复数）来表示刚体三维旋转的方法。它由四个实数分量组成：q = [q_w, q_x, q_y, q_z]^T，满足约束 ||q|| = 1（单位四元数）。其核心优势在于：相比于欧拉角，四元数表示法能无奇异地（singularity-free）表示飞行器在所有可能姿态下的方位，避免了欧拉角表示法在特定姿态（如万向节锁）下的奇异性问题。 | [
"第一步：识别问题核心是定义“四元数姿态表示法”。",
"第二步：从文本摘要部分提取定义：它是使用单位四元数（unit-quaternion）来表示刚体旋转的方法。",
"第三步：提取约束条件：四元数需满足单位范数（范数为1）。",
"第四步：从文本摘要和引言部分提取其与欧拉角的对比优势：无奇异性（singularity-free）。"
] | 2407.01275 | mimo | null | null | null | needs_review | {
"arxiv_id": "2407.01275",
"title": "Quaternion based Adaptive Backstepping Fast Terminal Sliding",
"authors": [],
"year": null,
"paper_path": "2407.01275_Quaternion_based_Adaptive_Backstepping_Fast_Terminal_Sliding",
"text_offset": 0
} | 该题考察对四元数姿态表示这一核心概念的精确记忆，包括其数学本质（单位四元数约束）和相对于欧拉角的关键优势（无奇异性），满分标准为答案完整包含定义和全部条件。 | [
"可能遗漏四元数分量构成或单位约束条件。",
"可能未明确说明“无奇异性”这一核心优势，或与文本描述不完全一致。"
] | passed | The paper states: 'Controllers designed based on unit-quaternion are singularity-free for attitude representation compared to other methods (e.g., Euler angles), which fail to represent the vehicle’s attitude at multiple orientations.' This directly supports the answer. | 0.95 | passed | passed | 1 | 0.95 | The paper states: 'Controllers designed based on unit-quaternion are singularity-free for attitude representation compared to other methods (e.g., Euler angles), which fail to represent the vehicle’s attitude at multiple orientations.' The answer correctly reflects this. | The paper states: 'Controllers designed based on unit-quaternion are singularity-free for attitude representation compared to other methods (e.g., Euler angles), which fail to represent the vehicle’s attitude at multiple orientations.' The answer correctly identifies the core advantage of quaternion representation as b... | arxiv-only | null | null | null | null | null | null | null | null |
CS-EVO-00032 | C | L3 | [
"classical"
] | 在论文描述的离散时间Stackelberg均值场博弈框架中，假设领导者为最大化社会福利而设定疫苗补贴，若追随者群体对疫苗的偏好参数（即单位效用）发生变化，这会如何影响Stackelberg均值场均衡下领导者的最优补贴策略？ | 基准条件：追随者类型为感染状态，偏好参数γ影响疫苗效用，领导者目标为max_{π_L} E[∑_t (W(t) - C_s(t))]，其中W(t)为社会福利，C_s(t)为补贴成本。追随者在均衡下最大化自身奖励到go：J_F(x_F, μ; π_L)。变化条件：偏好参数从γ增至γ' > γ。追随者最优响应中，疫苗选择概率随γ增加而上升。多方案对比：1) γ增大：追随者自发接种意愿增强，领导者可降低补贴幅度以维持相同接种率，补贴成本下降，但社会福利可能因外部性而变化；2) γ减小：追随者意愿降低，领导者需提高补贴以激励接种，成本增加。工程结论：领导者最优补贴策略与追随者偏好参数γ负相关，即γ增大时最优补贴降低。敏感性分析表明系统对γ变... | [
"基准条件复述：原模型中，追随者类型x_F服从受控马尔可夫过程，偏好参数γ影响疫苗效用项；领导者优化问题为max_{π_L} E[∑_t (W(t) - C_s(t))]，其中C_s(t)与补贴率正相关。",
"追随者最优响应：在给定π_L下，追随者均衡策略π_F*最大化J_F(x_F, μ; π_L)，疫苗选择概率p_vacc随γ增加而单调递增（因为效用增加）。",
"变化条件分析：比较γ和γ' (>γ)，在相同π_L下，追随者接种概率p_vacc(γ') > p_vacc(γ)。因此，为达到目标接种率，领导者可降低补贴。",
"多方案对比：若γ增大，领导者可降低补贴，成本C_s下降；若γ减小，领导者需提高补贴... | 2201.05959 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2201.05959",
"title": "Master Equation for Discrete Time Stackelberg Mean Field Gam",
"authors": [],
"year": null,
"paper_path": "2201.05959_Master_Equation_for_Discrete_Time_Stackelberg_Mean_Field_Gam",
"text_offset": 0
} | 考察在Stackelberg均值场博弈中，追随者偏好参数变化对领导者最优策略的敏感性，需基于模型进行多方案对比和工程结论。 | [
"未清晰列出基准和变化条件的数值对比或量化关系",
"未明确给出至少两种参数变化方向的对比分析",
"工程结论未直接关联模型或缺乏明确敏感性判定"
] | passed | The paper does not provide a specific model with a preference parameter γ affecting vaccine utility, nor does it analyze how changes in such a parameter affect the leader's optimal subsidy. The epidemic example in Section V-A describes followers' types as infection states, but no parameter γ is mentioned. The leader's ... | 0.95 | passed | passed | 0.9 | 0.8 | The paper discusses a Stackelberg mean field game with a leader and followers, and includes an epidemic model where the leader chooses subsidies for a vaccine to maximize social welfare. The answer's reasoning about the leader adjusting subsidies based on follower preferences is consistent with the paper's framework, t... | The paper's abstract and introduction describe an epidemic model where 'The leader chooses subsidies for a vaccine to maximize social welfare and minimize vaccination costs.' The answer correctly interprets this as a Stackelberg mean field game where the leader's optimal policy (subsidy) depends on follower behavior, w... | redistributable | [
"The answer introduces a preference parameter γ not present in the paper.",
"The paper does not discuss how changes in follower preferences affect the leader's optimal subsidy.",
"The answer's multi-scenario comparison and engineering conclusions are not derived from the paper."
] | [
"The answer introduces a specific parameter γ not defined in the paper excerpt, but this is a reasonable domain-specific extension for the epidemic example mentioned in the abstract.",
"The answer's conclusion that the optimal subsidy is negatively correlated with follower preference is a logical inference from t... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | [
"The answer introduces a parameter γ not explicitly defined in the provided paper excerpt, but this is acceptable as domain knowledge."
] |
CS-EVO-00033 | D | L4 | [
"nonlinear",
"robust",
"digital"
] | 针对一类反应扩散偏微分方程（PDE），设计一个性能屏障事件触发控制（P-ETC）方案，使其满足：1）全局指数收敛至零（空间L2范数意义下）；2）无Zeno现象；3）控制更新次数少于常规事件触发控制（R-ETC）。请给出完整的控制方案设计，包括数学模型、控制器结构、触发机制和参数整定方法。 | 1. 系统建模：考虑一维反应扩散PDE：u_t = α u_xx + β u + b u(1, t) + γ w(t)，空间域x∈[0,1]，边界条件u_x(0,t)=0，u(1,t)=w(t)。α,β,γ,b为已知常数。
2. 控制器选型：采用PDE反步法设计控制律w(t)=k(z(0,t))，其中k为稳定核函数，z为反步变换后的目标PDE系统状态。选择P-ETC而非R-ETC，因其允许Lyapunov函数在性能屏障V_b(t)内短暂增加，以减少触发次数。
3. 参数整定：定义性能屏障V_b(t)=V(0)e^{-λt}，λ>0。触发条件为：|V(t) - V_b(t)| ≥ εV_b(t)，ε∈(0,1)为容忍因子。控制器增益k... | [
"定义反应扩散PDE模型及其边界条件。",
"基于PDE反步法设计控制律w(t)=k(z(0,t))，并说明控制器增益k的表达式。",
"引入性能屏障V_b(t)和触发条件|V(t)-V_b(t)|≥εV_b(t)，并解释P-ETC如何允许Lyapunov函数短暂增加以减少触发。",
"证明闭环系统满足指数稳定性，并推导避免Zeno现象的最小驻留时间条件。",
"讨论工程实现中的测量、通信约束及参数调整注意事项。"
] | 2407.08178 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案设计是否基于论文内容，技术路线是否合理可行。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "是否正确选择P-ETC并说明其相对于R-ETC的优势，控制方法与问题是否匹配。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否涵盖... | needs_review | {
"arxiv_id": "2407.08178",
"title": "Performance Barrier Event Triggered Control of a Class of Re",
"authors": [],
"year": null,
"paper_path": "2407.08178_Performance_Barrier_Event_Triggered_Control_of_a_Class_of_Re",
"text_offset": 0
} | 该题考察针对PDE系统设计P-ETC完整方案的能力，包括建模、控制律设计、触发机制、参数整定和性能分析，要求结合论文核心概念进行工程化设计。 | [
"未完整包含所有设计环节（如缺少参数整定或工程考量）。",
"数学模型或控制器表达式有误或不完整。",
"未能准确阐述P-ETC相比R-ETC的触发次数减少机制。",
"未分析避免Zeno现象的条件或性能验证不充分。"
] | rejected | The paper does not consider the PDE model u_t = α u_xx + β u + b u(1,t) + γ w(t) with boundary conditions u_x(0,t)=0, u(1,t)=w(t). Instead, it considers a reaction-diffusion PDE with boundary actuation and sensing, specifically in Section 2: 'Consider the reaction-diffusion PDE... u_t(x,t) = ε u_xx(x,t) + λ u(x,t), wit... | 0.95 | rejected | rejected | 0.95 | 0.9 | The paper does not consider the PDE model u_t = α u_xx + β u + b u(1,t) + γ w(t) with boundary conditions u_x(0,t)=0, u(1,t)=w(t). The paper's model is a reaction-diffusion PDE with boundary actuation and sensing, but the specific form and parameters given in the answer are not present. The controller structure and par... | The paper's abstract and introduction describe the P-ETC scheme for a 'class of reaction-diffusion PDEs' but do not specify the exact PDE model, boundary conditions, or controller structure given in the answer. The answer's specific model (u_t = α u_xx + β u + b u(1, t) + γ w(t)) and controller (w(t)=k(z(0,t))) are not... | redistributable | [
"The PDE model and boundary conditions do not match the paper.",
"The control law is incorrectly specified; the paper uses a backstepping controller with integral form.",
"The triggering condition is incorrect; the paper uses e(t) ≤ 0 with a dynamic variable.",
"The minimum inter-event time formula is not gen... | [
"The answer provides a specific PDE model, controller structure, and triggering condition that are not found in the provided paper excerpt. While the answer's concepts (P-ETC, backstepping, performance barrier) are consistent with the paper's domain, the detailed design is fabricated and not verifiable from the sou... | null | null | null | null | null | [
"The PDE model in the answer does not match the paper's model.",
"The controller gain formula is not from the paper.",
"The triggering condition and minimum inter-event time are not as stated in the paper.",
"The answer invents specific parameter tuning steps not present in the paper."
] |
CS-EVO-00034 | C | L4 | [
"modern",
"nonlinear"
] | 在DeepMartNet算法中，对于Dirichlet特征值问题，若将随机过程dX_t = μdt + σ·dB_t中的漂移项μ从μ₀增加到1.5μ₀，同时保持扩散项σ不变，分析由此变化对基于马尔可夫性质的损失函数设计产生的影响，并给出相应的敏感性判定。 | 基准条件：原系统参数为漂移项μ₀，扩散项σ，定义随机过程dX_t = μ₀dt + σ·dB_t，对应的椭圆算子生成器为L = μ₀ᵀ∇ + ½Tr(σσᵀ∇∇ᵀ)。变化条件：漂移项变为1.5μ₀，扩散项σ不变，新过程为dX_t = 1.5μ₀dt + σ·dB_t，新生成器L' = (1.5μ₀)ᵀ∇ + ½Tr(σσᵀ∇∇ᵀ)。变化前后的差异在于漂移项μ增加了50%，这直接影响算子L中的梯度项系数。基于马尔可夫性质的损失函数依赖于从算子L生成的随机过程X_t的采样。当μ增大时，随机过程的期望漂移速度加快，导致过程X_t在相同时间内更倾向于离开定义域D，从而影响马尔可夫鞅过程M_t = u(X_t) - u(x₀) - ∫₀ᵗ(λ... | [
"步骤1：确定基准条件下的随机过程生成器L与鞅M_t的表达式。",
"步骤2：量化分析漂移项μ从μ₀增至1.5μ₀后，对生成器L中梯度项系数的直接影响。",
"步骤3：分析该变化如何改变随机过程X_t的期望轨迹，进而影响基于马尔可夫性质的损失函数采样。",
"步骤4：对比μ增大和μ减小两种变化方向对算法采样策略和收敛性的不同影响。",
"步骤5：基于上述分析，给出明确的敏感性判定和针对工程实践的调整建议。"
] | 2307.11942 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2307.11942",
"title": "DeepMartNet A Martingale based Deep Neural Network Learni",
"authors": [],
"year": null,
"paper_path": "2307.11942_DeepMartNet_A_Martingale_based_Deep_Neural_Network_Learni",
"text_offset": 0
} | 该题考察在随机最优控制背景下，模型参数（漂移项）变化对基于马尔可夫性质的神经网络损失函数设计的影响，要求进行完整的敏感性分析、多方案对比并给出工程结论。 | [
"未明确列出变化前后的具体参数对比（如1.5μ₀）。",
"分析未紧扣损失函数（基于马尔可夫性质）的具体影响，仅泛泛而谈过程变化。",
"多方案对比不完整，仅描述了一个方向或缺少对比。",
"工程结论不明确或缺乏可操作性建议。"
] | passed | The paper does not discuss the effect of changing the drift coefficient μ on the loss function design or sensitivity analysis. The Martingale property (2.6)-(2.11) is derived for a fixed μ and σ, and no analysis of parameter variations is provided. | 0.95 | passed | passed | 0.9 | 0.9 | The paper defines the stochastic process (2.3) with drift μ and diffusion σ, and the Martingale M_t in (2.6) depends on the process X_t. The answer correctly identifies that changing μ alters the generator L and the process dynamics, affecting the sampling distribution and the Martingale property. The paper does not ex... | Section 2.1 defines the stochastic process dX_t = μdt + σ·dB_t (Eq. 2.3) and the associated elliptic operator L = μᵀ∇ + ½Tr(σσᵀ∇∇ᵀ) (Eq. 2.2). The loss function is based on the Martingale property of M_t = u(X_t) - u(x₀) - ∫₀ᵗ(λ - V(X_s))u(X_s)ds (Eq. 2.6), whose expectation is constant (Eq. 2.11). The answer correctly... | redistributable | [
"The answer speculates on the impact of changing μ without any support from the paper.",
"The paper does not mention sensitivity analysis or adaptive sampling strategies.",
"The answer introduces concepts (e.g., 'sampling time step adjustment', 'adaptive sampling') not present in the source."
] | [
"Minor: The answer's discussion of sensitivity and engineering recommendations (e.g., adjusting sampling time steps) is reasonable domain knowledge but goes beyond the explicit content of the provided paper excerpt, which does not analyze parameter sensitivity or propose adaptive strategies."
] | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00035 | D | L4 | [
"classical",
"digital"
] | 针对论文中描述的重型四旋翼无人机在移动船只上降落的场景，设计一个完整的PID姿态控制系统（俯仰通道），以确保无人机在遭遇垂直振荡和横风干扰时，能将俯仰角跟踪误差控制在±2°以内，且调节时间小于1秒。 | 1. 系统建模：基于论文中描述的四旋翼动力学，俯仰通道简化模型为：Jθ θ̈ = uθ，其中 Jθ 为俯仰转动惯量，uθ 为俯仰力矩控制输入。考虑风扰动 d(t) 和船体垂直振荡引起的姿态误差 e_d(t)，则模型为 Jθ θ̈ = uθ - Jθ d(t) - Jθ e_d(t)。
2. 控制器选型：选用PID控制器，因为其结构简单、实时性好，适用于论文中提到的实时控制系统，且能通过积分项消除常值扰动。控制律为 uθ = Kp(θ_ref - θ) + Ki ∫(θ_ref - θ)dt + Kd(θ̇_ref - θ̇)。
3. 参数整定：基于文献中类似模型参数（如 Jθ = 0.01 kg·m²），采用Ziegler-Nich... | [
"基于论文描述，建立俯仰通道简化动力学模型，包含转动惯量、控制力矩和扰动项。",
"选用PID控制器，因其适用于论文中的实时控制场景，并能处理积分误差。",
"采用Ziegler-Nichols方法整定PID参数，给出具体数值和理论依据。",
"通过传递函数分析闭环系统性能，包括稳定裕度、响应时间和误差指标。",
"讨论实际实现中的约束，如执行器饱和、传感器噪声和计算频率要求。"
] | 2411.05445 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否基于论文描述的无人机和场景，技术路径是否可行。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型是否合理，理由是否充分，是否匹配控制目标。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否覆盖建模、选型、整定、验... | needs_review | {
"arxiv_id": "2411.05445",
"title": "Agile UAV landing control on moving ship in adverse conditio",
"authors": [],
"year": null,
"paper_path": "2411.05445_Agile_UAV_landing_control_on_moving_ship_in_adverse_conditio",
"text_offset": 0
} | 该题考察针对特定工程场景（移动平台上的无人机降落）设计完整姿态控制方案的能力，包括建模、控制器设计、参数整定、性能分析和工程实现考量，要求方案具体、参数可验证、分析全面。 | [
"建模部分若遗漏扰动项或简化过度，可能导致方案不完整。",
"控制器选型理由不充分或未与论文场景关联。",
"参数整定过程缺失或数值不合理，未基于理论方法。",
"性能分析未覆盖所有关键指标（如稳定裕度、响应时间、稳态误差）或计算错误。",
"工程考量未涉及执行器限制、传感器处理或实时性等实际约束。"
] | passed | The paper does not provide specific quadrotor dynamics equations, PID controller design, or parameter tuning details. It only mentions using a PID flight control system based on reference-point tracking, but no explicit model or controller parameters are given. The answer invents numerical values (Jθ=0.01, Ku=10, Tu=0.... | 0.95 | passed | passed | 0.9 | 0.8 | The paper describes a PID flight control system based on reference-point tracking for a quadrotor UAV, including realistic saturation limits and disturbance handling. The answer designs a PID controller for the pitch channel, which is consistent with the paper's approach. The paper does not provide specific PID gains o... | The paper states: 'The PID flight control system is proposed based on reference-point tracking, allowing the UAV to follow any desired path in 3D space whilst simultaneously yawing to face any desired heading.' and 'Realistic saturation limits on actuator outputs to ensure the real-world performance of actuators.' The ... | redistributable | [
"The paper does not provide a simplified pitch dynamics model Jθ θ̈ = uθ.",
"No specific PID gains or tuning method (Ziegler-Nichols) are mentioned.",
"The numerical values for Jθ, Ku, Tu, Kp, Ki, Kd are fabricated.",
"The closed-loop transfer function and performance metrics (phase margin, gain margin, settl... | [
"The answer's simplified model (Jθ θ̈ = uθ) omits the coupling effects and nonlinear dynamics typical of a quadrotor, which the paper implies by discussing a full 3D control system. However, for a single-channel design question, this simplification is a reasonable engineering approach and does not contradict the pa... | null | null | null | null | null | null |
CS-EVO-00036 | B | L3 | [
"classical",
"robust"
] | 考虑一个简化的单电池模组，其状态空间模型为：dx/dt = Ax + Bu，y = Cx。其中状态x = [SOC, T]^T（SOC为荷电状态，T为温度），输入u为充电电流I_ch，参数矩阵为A = [[-0.01, 0.001], [0.005, -0.02]]，B = [[0.002], [0.001]]，C = [[1, 0]]。假设系统初始状态x0 = [0.8; 25]，在t=0时刻，攻击者通过篡改BMS传感器读数，使得系统实际接收到的输出测量值y_meas = y + a(t)，其中a(t) = 0.1（常数偏移攻击）。若BMS基于该受污染的测量值y_meas，采用状态反馈控制律u = -K*x_hat，且设计增益K使... | 系统矩阵A的特征值为λ1≈-0.013，λ2≈-0.017，系统开环稳定。参考值y_ref=0.8，对应开环稳态输入u_ref满足0 = A*x_ss + B*u_ref，y_ref = C*x_ss，解得x_ss = [0.8; 24.75]，u_ref = -0.01。攻击者篡改输出y_meas = y + 0.1，BMS基于y_meas估计状态x_hat并实施反馈u = -K*x_hat，闭环期望极点-0.1，-0.2，可解得K。为使输出y(t)跟踪y_ref=0.8，攻击者需施加输入攻击u_a(t)，使系统状态轨迹满足dx/dt = A*x + B*(u_ref + u_a(t))，且输出y = C*x = 0.8恒成立。将... | [
"第一步：基于给定参数矩阵A、B、C和参考输出y_ref=0.8，计算开环稳态状态x_ss和输入u_ref。由0=A*x_ss+B*u_ref和y_ref=C*x_ss，解得x_ss=[0.8; 24.75]，u_ref=-0.01。",
"第二步：分析隐蔽攻击条件。攻击者通过输出偏移a(t)=0.1污染测量值y_meas，为使实际输出y(t)=C*x(t)仍跟踪y_ref=0.8，需满足C*x(t)=0.8恒成立，即SOC恒为0.8。",
"第三步：将SOC恒为0.8的条件代入状态方程第一行：d(SOC)/dt = A(1,1)*SOC + A(1,2)*T + B(1)*(u+u_a(t)) = 0。已知u采用基... | 2401.13801 | mimo | null | null | null | needs_review | {
"arxiv_id": "2401.13801",
"title": "Exploring Adversarial Threat Models in Cyber Physical Batter",
"authors": [],
"year": null,
"paper_path": "2401.13801_Exploring_Adversarial_Threat_Models_in_Cyber_Physical_Batter",
"text_offset": 0
} | 该题考察从网络化控制系统（CPBS）的对抗性威胁模型出发，结合状态空间表示、反馈控制设计及隐蔽攻击条件，进行多步数学推导以推导攻击信号表达式的能力，综合应用了状态反馈控制、系统建模和对抗分析。 | [
"未能正确建立或求解开环稳态条件，导致初始推导错误。",
"未能正确理解并应用隐蔽攻击条件（输出恒为参考值），导致推导方向偏离。",
"在推导u_a(t)表达式时，未能清晰隔离出攻击者可控部分并给出最终结果。",
"计算过程有误，导致最终数值结果错误。"
] | passed | The source paper does not provide any specific state-space model, parameter matrices, or control design details. The paper focuses on adversarial threat models for battery systems but does not include the numerical example or derivations presented in the answer. Therefore, the answer is not factually supported by the p... | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses adversarial attack generation in battery systems, focusing on stealthy attacks that manipulate sensor readings while remaining undetected. The answer describes a scenario where an attacker injects a constant offset into the output measurement and derives an input attack signal to maintain the output... | The paper discusses adversarial threat models for cyber physical battery systems, focusing on attack generation policies and stealthiness. The answer correctly applies control theory concepts (state-space models, feedback control, attack signals) consistent with the paper's domain of analyzing adversarial dynamics in b... | arxiv-only | [
"The answer invents a specific state-space model and parameters not present in the paper.",
"The derivation of input attack signal u_a(t) is not based on any content from the paper.",
"The paper does not discuss state feedback control design or pole placement for battery systems."
] | [
"Minor: The answer's numerical calculations (e.g., eigenvalues, steady-state values) are not verified against the paper, but this is acceptable as the paper does not provide specific numerical examples for this scenario."
] | null | null | null | null | null | null |
CS-EVO-00039 | C | L2 | [
"intelligent",
"optimal"
] | 在本文提出的基于安全深度强化学习的建筑供暖控制框架中，如果将实时自适应安全滤波器（real-time adaptive safety filter）中用于约束满足的预测时间窗口（prediction time window）缩短，对系统在提供需求侧灵活性时满足运营商灵活性请求的能力（即约束满足度）会产生什么影响？ | 1. 基准条件复述：原框架采用深度确定性策略梯度（DDPG）算法，通过实时自适应安全滤波器保证系统在需求侧灵活性提供期间满足运营商施加的能量约束。该安全滤波器依赖于预测时间窗口来评估未来状态并确保约束满足。文中未明确给出窗口长度的具体数值，但强调其“实时”与“自适应”特性。
2. 变化条件分析：将预测时间窗口从基准长度（假设为T秒）缩短至T'秒（T' < T）。缩短窗口意味着控制器只能基于更近期的未来信息进行安全校正。
3. 多方案对比：
a) 窗口显著缩短（T' << T）：控制器对更远期的约束违反风险感知能力下降，可能导致在灵活性请求执行期间出现短时约束违反，但可能降低计算负担。
b) 窗口略微缩短（T' ≈ T但T... | [
"基准条件复述：识别原框架核心组件（DDPG + 实时自适应安全滤波器）及其功能（保证约束满足）。",
"变化条件分析：定义变化（缩短预测时间窗口）并指出其直接影响（可用于预测的信息时域变短）。",
"多方案对比：分析窗口显著缩短与略微缩短两种情景下的不同影响机制。",
"工程结论：总结敏感性关系（正相关）并给出工程建议。"
] | 2604.16033 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2604.16033",
"title": "Safe Deep Reinforcement Learning for Building Heating Contro",
"authors": [],
"year": null,
"paper_path": "2604.16033_Safe_Deep_Reinforcement_Learning_for_Building_Heating_Contro",
"text_offset": 0
} | 考察对安全强化学习控制框架中关键设计参数（预测时间窗口）的敏感性分析能力，需结合文中框架描述进行多方案推理。 | [
"未能清晰复述基准条件（如明确安全滤波器的功能）。",
"变化条件分析未量化或对比具体影响。",
"多方案对比不充分或未涉及不同缩短程度。",
"工程结论未明确敏感性判定或建议。"
] | passed | The paper does not discuss the effect of shortening the prediction time window of the real-time adaptive safety filter. The filter is described as 'real-time adaptive' but no details on its prediction horizon or sensitivity to window length are provided. The answer invents a sensitivity analysis not present in the pape... | 0.95 | passed | passed | 0.9 | 0.9 | The paper introduces a real-time adaptive safety filter to ensure compliance with flexibility requests, but does not specify the prediction time window length or analyze its impact. The answer's reasoning about shortening the window reducing constraint satisfaction is consistent with general control theory and does not... | The paper states: 'To address safety concerns with reinforcement learning, particularly regarding compliance with flexibility requests, we propose a real-time adaptive safety-filter to ensure that the system operates within predefined constraints during demand-side flexibility provision.' and 'The proposed real-time ad... | redistributable | [
"The paper does not specify a prediction time window or analyze its impact on constraint satisfaction.",
"The answer introduces hypothetical scenarios (e.g., T' << T) not supported by the paper.",
"The conclusion about positive correlation between window length and constraint satisfaction is not derived from th... | [
"The answer correctly notes that the paper does not specify the exact length of the prediction window, which is accurate based on the provided excerpt."
] | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00040 | D | L4 | [
"multi_agent"
] | 针对具有单积分动力学且通信拓扑为时变强连通有向图的多智能体系统，请设计一个基于空中计算共识的分布式控制方案，以实现期望的编队队形并确保智能体间的安全避碰。要求：1）编队误差在5秒内收敛到小于0.1米；2）任意两智能体间的最小安全距离需大于0.5米；3）控制输入需满足幅值约束|u_i| ≤ 1.5 m/s。 | 1. 系统建模：第i个智能体的动力学模型为 dot{x}_i(t) = u_i(t)，其中x_i ∈ ℝ^d为位置，u_i为控制输入。通信拓扑由时变有向图G(t) = (N, A(t))描述，其邻接矩阵为W(t)。
2. 控制器选型：采用基于人工势场法和空中计算共识协议的分布式控制律。选择理由：人工势场法可提供避碰的梯度力，空中计算共识能利用无线信道叠加特性高效实现多智能体状态平均。
3. 参数整定：定义期望编队中心点为p_c，单个智能体的控制律为 u_i(t) = -k_c * sum_{j∈N_i(t)} w_{ij}(t)(x_i(t) - x_j(t)) + sum_{j∈N_i(t)} g_{ij}(t)(x_j(t) ... | [
"第一步：将智能体动力学建模为单积分器，并明确通信拓扑为时变强连通有向图。",
"第二步：确定控制目标（编队形成与避碰）并选择将人工势场法与空中计算共识协议相结合的控制框架。",
"第三步：设计包含共识项、编队跟踪项和避碰梯度项的分布式控制律公式。",
"第四步：给出控制律中关键参数（如k_c, k_p）的初步取值，并基于李雅普诺夫分析和势场函数特性进行整定，以满足收敛时间与安全距离指标。",
"第五步：分析控制律的稳定性，并验证其性能指标（收敛速度、避碰、输入约束）在理论上可实现。",
"第六步：讨论实际部署中影响方案可行性的关键工程因素，如通信约束与传感需求。"
] | 2403.14386 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在给定的单积分动力学和通信约束下是否可行，控制律是否能同时处理编队与避碰。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择人工势场与空中计算共识相结合的方法是否合理，并能有效解决题目要求。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"descript... | needs_review | {
"arxiv_id": "2403.14386",
"title": "Exploiting Over The Air Consensus for Collision Avoidance an",
"authors": [],
"year": null,
"paper_path": "2403.14386_Exploiting_Over_The_Air_Consensus_for_Collision_Avoidance_an",
"text_offset": 0
} | 该题考察为复杂多智能体系统设计完整分布式控制方案的能力，涵盖建模、控制器设计、参数整定、性能分析和工程实现。满分标准为提供逻辑连贯、数学完整且切实可行的五段式方案，各项指标均得到理论或数值支撑。 | [
"控制律公式不完整或数学表达有误。",
"参数整定过程缺乏依据，未结合性能指标进行解释。",
"性能验证部分仅定性描述，未给出定量分析或与设计要求的对应关系。",
"工程考量过于泛泛，未针对空中计算共识或避碰的具体挑战提出措施。"
] | passed | The paper does not provide a specific control law with numerical gains, convergence time bounds, or saturation constraints. It only proves asymptotic convergence for time-varying strongly connected digraphs using OtA consensus and potential fields, but without explicit performance guarantees like 5-second convergence o... | 0.95 | passed | passed | 0.85 | 0.8 | The paper proposes a distributed control method using Over-the-Air Consensus for agents with single-integrator dynamics, formation control, and collision avoidance via artificial potential fields. The answer correctly adopts these concepts, including the use of consensus and potential fields. The paper does not specify... | The paper's abstract and introduction state the system uses 'decoupled single-integrator dynamics' and 'Over the Air Consensus (OtA-Consensus)' for 'formation achievement and collision avoidance' using 'artificial potential fields'. The answer correctly models the dynamics as dot{x}_i = u_i, proposes a control law comb... | redistributable | [
"The answer invents specific numerical gains (k_c=2.0, k_p=3.0) and a potential function with d_safe=0.6m not present in the paper.",
"The answer claims convergence within 5 seconds to error <0.1m, which is not supported by the paper's asymptotic convergence result.",
"The answer includes control input saturati... | [
"The answer's specific control law structure (e.g., the exact terms and gains) is not detailed in the provided paper excerpt, but this is acceptable as a design synthesis. The paper does not specify the exact performance metrics (5s convergence, 0.1m error, 0.5m safety distance, 1.5 m/s input limit), so the answer'... | null | null | null | null | null | [
"The paper does not provide specific numerical values for gains or convergence time guarantees; the answer's claims (e.g., 5 seconds, 0.1 m) are not directly supported by the paper.",
"The control law in the answer includes terms not explicitly in the paper (e.g., k_p(p_c - x_i) and the specific potential functio... |
CS-EVO-00041 | B | L4 | [
"adaptive",
"mpc"
] | 考虑一个不确定离散时间线性系统 x_{t+1} = A x_t + B u_t + w_t，其中 w_t 是加性扰动。STT-MPC算法使用最小二乘估计器在线辨识系统动态 (Â_t, B̂_t)，并通过求解一个带有多面体管的MPC问题来生成控制输入 u_t，以满足状态和输入约束。为保证算法的递归可行性和渐近稳定性，必须确保所设计的多面体管能够覆盖由估计误差和未建模扰动引起的轨迹偏差。假设在一步预测中，系统真实动态与估计动态之间的偏差为 δA = A - Â_t 和 δB = B - B̂_t，且扰动 w_t 满足 ||w_t|| ≤ ε_w。请推导一步预测误差 e_{t+1} = x_{t+1} - x̂_{t+1} 的上界范数表示... | 一步预测误差 e_{t+1} 满足 ||e_{t+1}|| ≤ ||δA|| · ||x_t|| + ||δB|| · ||u_t|| + ||w_t|| ≤ ||δA|| · ||x_t|| + ||δB|| · ||u_t|| + ε_w。此不等式提供了误差上界的显式表示，是设计多面体管以包裹预测误差轨迹的基础。 | [
"第一步：写出一步预测误差 e_{t+1} = x_{t+1} - x̂_{t+1} 的定义。",
"第二步：将系统动态 x_{t+1} = A x_t + B u_t + w_t 和估计动态 x̂_{t+1} = Â_t x_t + B̂_t u_t 代入定义。",
"第三步：整理得到 e_{t+1} = (A - Â_t) x_t + (B - B̂_t) u_t + w_t = δA x_t + δB u_t + w_t。",
"第四步：对上式两边取范数，并利用三角不等式得到 ||e_{t+1}|| ≤ ||δA x_t|| + ||δB u_t|| + ||w_t||。",
"第五步：利用范数的相容性... | 2310.04842 | mimo | null | null | null | needs_review | {
"arxiv_id": "2310.04842",
"title": "Sub linear Regret in Adaptive Model Predictive Control",
"authors": [],
"year": null,
"paper_path": "2310.04842_Sub_linear_Regret_in_Adaptive_Model_Predictive_Control",
"text_offset": 0
} | 该题考察对自适应MPC中在线辨识误差传播的定量分析能力，需要从系统定义出发，通过代数推导和范数性质，得出预测误差的上界表达式。满分标准为推导过程完整、每步逻辑清晰、最终结果准确。 | [
"在第三步整理时，可能错误组合动态方程。",
"在第四步或第五步取范数时，可能未正确应用三角不等式或范数相容性性质。",
"最终表达式可能遗漏扰动项 ||w_t|| 或其上界 ε_w。"
] | passed | The source paper does not provide a derivation or explicit formula for the one-step prediction error bound. The paper focuses on the algorithm's regret analysis and stability properties, but does not detail the specific error bound expression given in the answer. | 1 | passed | passed | 0.95 | 0.9 | The paper discusses STT-MPC using polytopic tubes to handle uncertainties from estimation errors and disturbances. The derivation of the one-step prediction error bound is a standard result consistent with the paper's framework, though not explicitly stated in the excerpt. | The paper describes STT-MPC as combining the certainty-equivalence principle with polytopic tubes to handle uncertainties from estimation errors and disturbances. The answer correctly derives the one-step prediction error bound using the triangle inequality, which is a standard and necessary step for tube-based MPC des... | redistributable | [
"The answer presents a specific inequality for the prediction error that is not derived or stated in the source paper. The paper does not provide such a detailed error bound derivation."
] | [
"API error: Error code: 429 - {'error': {'code': '429', 'message': 'Too many requests', 'type': 'limitation'}}"
] | [
"B维答案缺少推导结论标记（未找到\"解得\"\"得到\"\"因此\"等结果标记）"
] | null | null | null | null | null |
CS-EVO-00042 | C | L3 | [
"robust",
"optimal"
] | 在论文提出的直接数据驱动控制框架中，若用于控制器综合的单条数据轨迹所含噪声的协方差矩阵 R 不再是恒定常数，而是随时间变化的，该框架的均方稳定性（MSS）保证和最优稳态协方差最小化结论是否依然成立？请分析其敏感性。 | 基准条件：原框架假设噪声协方差矩阵 R 为已知恒定常数，并纳入凸优化问题（SDP）以保证 MSS 和最小化稳态协方差。变化条件：假设 R 变为时变矩阵 R(t)。分析：1. MSS 保证的敏感性：原框架的稳定性结论依赖于基于固定 R 构建的 LMI 条件（式(5)或类似形式）。当 R 时变，原 LMI 可能不再满足，导致 MSS 保证可能失效。结论对 R 的恒定性假设敏感。2. 最优性结论的敏感性：SDP 目标函数基于固定 R 最小化稳态协方差（式(8)或类似形式）。若 R 时变，原固定权重矩阵 Q 和 R 的 LQR 成本函数定义改变，基于固定 R 求解的增益 K 不再是对应时变噪声环境的最优解，最优性结论不成立。多方案对比：a)... | [
"复述原框架核心假设：噪声协方差矩阵 R 为已知恒定常数，并作为参数用于构建 LMI 稳定性条件和 SDP 最优控制器综合问题。",
"分析变化条件：将 R 替换为时变矩阵 R(t)。",
"评估对 MSS 保证的影响：原稳定性分析基于固定 R 的 LMI，时变 R 可能破坏 LMI 成立条件，因此 MSS 保证可能不再成立。",
"评估对最优性的影响：原 SDP 问题中 R 是成本函数权重的一部分，其时变化改变了优化问题的定义，导致原解非最优。",
"进行多方案对比：讨论 R(t) 在有限范围内波动与剧烈变化两种情景下框架的适用性。",
"给出工程结论：明确结论对 R 恒定性假设的敏感性，并指出扩展方向... | 2505.06407 | mimo | environment | null | null | needs_review | {
"arxiv_id": "2505.06407",
"title": "Direct Data Driven Control Using Noisy Measurements",
"authors": [],
"year": null,
"paper_path": "2505.06407_Direct_Data_Driven_Control_Using_Noisy_Measurements",
"text_offset": 0
} | 考察对数据驱动控制框架中关键假设（噪声统计恒定）变化时，其理论保证（MSS和最优性）敏感性的分析能力，要求进行完整的多情景对比和工程结论。 | [
"未能准确指出原框架中 R 恒定性假设的具体作用位置（如 LMI 和 SDP 问题中的角色）。",
"对敏感性分析不完整，只分析了 MSS 或只分析了最优性。",
"多方案对比不足，未提供至少两种不同的参数变化方向或影响情景。",
"工程结论模糊，未给出明确的敏感性判定或改进方向建议。"
] | passed | The paper assumes a constant noise covariance matrix R throughout (e.g., Section III: 'noise statistics are known and constant'). No discussion of time-varying R is provided. The LMI conditions and SDP formulation rely on this constant assumption. | 0.95 | passed | passed | 0.9 | 0.9 | The paper assumes noise covariance R is constant (Section I: 'noise statistics directly into the controller synthesis'). The answer correctly identifies that the framework's MSS and optimality guarantees rely on this assumption, and that time-varying R would break them. This is consistent with the paper's scope and sta... | The paper's abstract states: 'Our approach guarantees mean-square stability (MSS) and optimal performance by leveraging convex optimization techniques that incorporate noise statistics directly into the controller synthesis.' The introduction further specifies the problem as handling 'noisy state measurements' and 'noi... | arxiv-only | [
"The paper does not address time-varying noise covariance; thus, the answer's analysis is speculative and not supported by the paper.",
"The answer claims the framework's conclusions are sensitive to R being time-varying, which is a reasonable inference but not based on any evidence from the paper.",
"The answe... | [
"Minor: The answer references specific equation numbers (e.g., (5), (8)) which are not present in the provided excerpt, but this is a minor stylistic issue and does not affect the factual correctness of the analysis."
] | [
"C维只有单一方向分析（仅有\"升高\"方向，缺少多方向对比）"
] | null | null | null | null | null |
CS-EVO-00043 | D | L3 | [
"nonlinear",
"optimal"
] | 针对一个具有两个子系统的离散时间切换线性系统，设计一个最大离手混合控制序列，使系统从初始状态 x(0) = [1, 0]^T 在 5 个时间步内转移到原点。假设子系统动力学为 A1 = [[0.9, 0.1], [0, 0.8]] 和 A2 = [[0.8, 0], [0.2, 0.9]]，连续控制输入矩阵为 B1 = B2 = [[1], [0]]。可容许的切换（离散控制）序列为 1→2 或 2→1，连续控制 u(k) 的幅度限制为 |u(k)| ≤ 1。请给出控制序列设计的具体算法步骤和性能验证方法。 | 设计算法步骤：1) 建立系统模型：x(k+1) = A_{σ(k)}x(k) + B_{σ(k)}u(k)，其中σ(k)∈{1,2}，u(k)∈[-1,1]。2) 将最大离手问题转化为混合整数线性规划(MILP)：定义二进制变量表示切换(非零u(k))和切换动作(σ(k)≠σ(k-1))，目标是最小化切换次数与非零控制次数之和，约束为状态转移方程、初始和终端状态、控制幅值限制及可容许切换集。3) 使用标准MILP求解器(如Gurobi)求解。性能验证：验证解出的控制序列是否满足|u(k)|≤1且切换在可容许集内；计算状态轨迹，确认x(5)≈0；统计切换次数和非零u(k)次数，确认为最小。 | [
"系统模型为离散时间切换线性系统，包含两个子系统动力学和控制输入矩阵。",
"控制目标是设计混合控制序列（切换σ(k)和连续控制u(k)）使状态在5步内归零。",
"控制约束包括可容许切换集（仅允许1→2或2→1）和控制幅度限制|u(k)|≤1。",
"最大离手目标是最小化切换次数与非零连续控制次数之和，这是一个非凸优化问题。",
"可将问题转化为MILP：引入二进制变量表示切换和非零控制，目标函数为这些变量之和，约束为状态方程和限制。",
"通过MILP求解器得到数值解后，需验证状态轨迹终端值和约束满足情况。"
] | 2601.17980 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否具有工程可实施性"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否适合问题"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否覆盖建模、设计、分析与验证流程"
},
"innovation": {
... | needs_review | {
"arxiv_id": "2601.17980",
"title": "On maximum hands off restricted hybrid control for discrete ",
"authors": [],
"year": null,
"paper_path": "2601.17980_On_maximum_hands_off_restricted_hybrid_control_for_discrete_",
"text_offset": 0
} | 该题考察被测试者针对离散时间切换线性系统设计最大离手混合控制方案的综合能力，包括问题转化、优化建模和验证，Judge满分标准为方案完整、算法可行、性能验证充分。 | [
"未明确将最大离手问题转化为MILP，或转化不正确。",
"未考虑可容许切换约束或控制幅值约束。",
"性能验证未包含状态终端值或约束满足检查。",
"算法步骤描述过于笼统，缺乏可操作性。"
] | passed | The paper does not provide a specific algorithm for a given system with numerical matrices; it presents a general algorithm using mixed-integer convex optimization with ℓ1-approximation and conditions like restricted isometry property. The answer incorrectly claims the problem is solved via MILP directly without mentio... | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses maximum hands-off hybrid control for discrete-time switched linear systems, involving minimization of switches and non-zero continuous controls. The answer correctly formulates the problem as a mixed-integer optimization, consistent with the paper's approach (Section 1 mentions mixed-integer convex ... | The paper states: 'An algorithm to design sparse hybrid control sequences by employing a mixed-integer convex optimization problem was presented. The optimization problem computes a sparsest hybrid control sequence employing ℓ1-approximation (i.e., a convex relaxation of ℓ0-norm).' The answer correctly describes formul... | arxiv-only | [
"The answer suggests using MILP directly to minimize ℓ0-norm, but the paper uses ℓ1-approximation (convex relaxation) and requires conditions for equivalence.",
"The answer does not mention the sufficient conditions (restricted isometry property, range space property) needed for the ℓ1-solution to coincide with t... | [
"Minor: The answer does not mention the paper's specific use of ℓ1-approximation or the conditions (restricted isometry property, range space property) under which ℓ0 and ℓ1 sparsity coincide, but this is acceptable as the answer provides a general algorithmic framework consistent with the paper's methodology."
] | null | null | null | null | null | null |
CS-EVO-00044 | A | L3 | [
"modern",
"robust"
] | 在论文提出的线性不确定模型中，状态空间表示的名义系统矩阵A和B的数学表达式是什么？ | 论文中未明确给出名义系统矩阵A和B的具体数学表达式。文中仅提到该模型用于描述四分之一车SAVGS系统，并旨在填补非线性多体模型与线性等效模型之间的差距，以表征未建模动态、参数变化和外部扰动。因此，无法提供A和B的精确数学表达式。 | [
"第一步：审题，问题要求给出线性不确定模型中名义系统矩阵A和B的数学表达式。",
"第二步：检查提供的论文内容，定位关于线性不确定模型描述的部分。",
"第三步：分析发现，摘要和引言部分仅说明了模型的目的（表征未建模动态、参数变化和外部扰动）和应用（用于LMI优化），但未提供状态空间方程的具体数学形式，也未列出A、B矩阵的元素或结构。",
"第四步：基于现有信息，A和B的数学表达式无法从给定文本中获取。"
] | 2401.06650 | mimo | null | null | null | needs_review | {
"arxiv_id": "2401.06650",
"title": "LMI based robust model predictive control for a quarter car",
"authors": [],
"year": null,
"paper_path": "2401.06650_LMI_based_robust_model_predictive_control_for_a_quarter_car",
"text_offset": 0
} | 该题考察对论文中核心控制模型（线性不确定模型）数学形式细节的记忆和理解，满分标准是准确指出论文未提供A、B矩阵的具体表达式并说明模型用途。 | [
"若回答者错误地编造了A、B矩阵的表达式，则完全扣分。",
"若回答者仅提到模型用途但未明确说明表达式缺失，则可能因信息不完整而扣分。",
"若回答者混淆了模型描述与具体数学形式，给出不准确的推断，则扣分。"
] | passed | The paper does not provide explicit mathematical expressions for the nominal system matrices A and B in the state-space representation. The answer correctly states that the paper does not give these expressions. | 0.95 | passed | passed | 0.95 | 0.9 | The paper does not explicitly provide the mathematical expressions for the nominal system matrices A and B in the state-space representation. The answer correctly states this fact. | The paper excerpt describes the proposed linear uncertain model and its purpose but does not provide the explicit mathematical expressions for the nominal system matrices A and B. The answer correctly states that the paper does not give these specific expressions. | arxiv-only | [] | null | [
"A维答案过于模糊：缺少 LaTeX 公式、条件-结论结构、或 ≥3 个控制科学术语",
" - 未检测到 LaTeX 公式标记",
" - 未检测到条件-结论结构",
" - 控制科学术语不足（仅 0/3）"
] | null | null | null | null | null |
CS-EVO-00045 | B | L2 | [
"robust",
"adaptive"
] | 考虑一个未知的连续时间线性系统，已从其采集到一组有限的带噪声状态测量值x(t)和输入值u(t)。基于这些数据设计一个无采样的状态反馈控制器u = -Kx，旨在实现闭环系统的输入到状态稳定性（ISS）。根据教材内容，为确保控制器在考虑网络采样时，仍能（近似）保持ISS特性，所设计的鲁棒数据驱动触发策略需要满足哪个关键条件以排除Zeno现象？ | 为排除Zeno现象，所设计的传输策略必须确保存在一个（全局）严格为正的最小事件间时间（minimum inter-event times）。这意味着两次连续数据传输之间的时间间隔存在一个大于零的下界，无论系统状态如何演化。 | [
"第一步：根据教材，事件触发控制的目标是在网络化场景中按需传输数据，以节约资源。",
"第二步：在为未知线性系统设计无采样ISS控制器u = -Kx后，需要考虑网络采样带来的影响。",
"第三步：教材明确指出，为处理采样引入的网络并（近似）保持原始稳定性，所设计的鲁棒数据驱动触发策略在存在扰动的情况下，必须保证存在一个（全局）严格为正的最小事件间时间。",
"第四步：这个条件是排除Zeno行为（即在有限时间内发生无限次传输）的必要保证。"
] | 2208.11634 | mimo | null | null | null | needs_review | {
"arxiv_id": "2208.11634",
"title": "Event triggered Control From Data",
"authors": [],
"year": null,
"paper_path": "2208.11634_Event_triggered_Control_From_Data",
"text_offset": 0
} | 该题考察对数据驱动事件触发控制中关键设计目标的理解，特别是鲁棒性条件与排除Zeno现象的关系，要求从系统描述出发，经过逻辑推导得出具体条件。 | [
"可能混淆“最小事件间时间”与具体的触发条件公式。",
"可能遗漏“全局”或“严格为正”等关键限定词。",
"可能将触发策略的具体形式（如绝对/相对阈值）误认为是排除Zeno的核心条件。"
] | passed | The paper states: 'In all cases, the designed transmission policies ensure the existence of a (global) strictly positive minimum inter-event times thereby excluding Zeno phenomenon despite disturbances.' This directly supports the answer. | 1 | passed | passed | 1 | 0.95 | The paper states: 'In all cases, the designed transmission policies ensure the existence of a (global) strictly positive minimum inter-event times thereby excluding Zeno phenomenon despite disturbances.' | The abstract states: 'In all cases, the designed transmission policies ensure the existence of a (global) strictly positive minimum inter-event times thereby excluding Zeno phenomenon despite disturbances.' The answer directly reflects this key condition. | arxiv-only | null | null | null | null | null | null | null | null |
CS-EVO-00046 | D | L4 | [
"adaptive",
"classical"
] | 基于教材中提出的同步导向自适应控制设计理念，为一个一阶线性不确定系统设计一个闭环参考模型自适应控制器。控制目标：使被控对象的输出跟踪参考模型输出，要求超调量小于10%，调节时间小于2秒，稳态误差为零。已知系统动态为 dx/dt = -θx + u，其中参数θ未知，但其标称值θ0=1，且|θ - θ0| ≤ Δ = 0.5。设计需明确同步耦合输入的结构和参考模型的具体形式。 | 1. 系统建模：被控对象：dx/dt = -θx + u，参考模型：xm/dt = -am xm + r，其中am > 0，r为有界参考输入。同步误差：e = x - xm。2. 控制器选型：采用闭环参考模型自适应控制（CRM-MRAC）。选择理由：通过反馈连接实现同步，改善瞬态性能。3. 参数整定：取am=2，确保收敛。控制器：u = -kx + v，其中v为同步耦合输入。自适应律：dθ/dt = γ e x。取γ=0.1。耦合输入设计为v = -k2 e，取k2=5，确保误差动态稳定。4. 性能验证：闭环误差动态：de/dt = -(am + k2)e。选择am=2，k2=5，使得误差时间常数τ = 1/(am+k2) = 1/... | [
"建立被控对象和参考模型的一阶线性数学模型。",
"定义同步误差e = x - xm。",
"选择CRM-MRAC作为控制方法，因其通过反馈实现同步。",
"将参考模型时间常数设为am=2，以保证收敛速度。",
"设计耦合输入v = -k2 e，与反馈项-kx组成控制律。",
"选择增益k2=5，使误差动态收敛时间常数τ=1/(am+k2)≈0.143秒。",
"验证调节时间4τ≈0.57秒满足小于2秒的要求。",
"说明自适应律dθ/dt = γ e x用于估计未知参数θ。"
] | 2403.09179 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "设计方案是否可行，是否基于教材的同步导向概念且数学模型正确。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "是否选择了恰当的控制方法（如CRM-MRAC）并说明了其与同步设计的关联。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "... | needs_review | {
"arxiv_id": "2403.09179",
"title": "Synchronisation Oriented Design Approach for Adaptive Contro",
"authors": [],
"year": null,
"paper_path": "2403.09179_Synchronisation_Oriented_Design_Approach_for_Adaptive_Contro",
"text_offset": 0
} | 考察基于同步理念的闭环参考模型自适应控制器的完整设计流程，包括建模、控制器设计、参数整定、性能分析和工程考量，要求方案具体且满足给定性能指标。 | [
"未明确给出控制器或耦合输入的具体数学表达式。",
"未计算或验证超调量、调节时间等具体性能指标是否达标。",
"参数整定过程缺乏依据，未说明选择am、k2等数值的理由。",
"工程考量部分过于简略，未讨论如参数漂移、未建模动态等实际挑战。"
] | passed | The paper discusses CRM-MRAC conceptually but does not provide explicit design formulas for a first-order system with unknown θ. The answer's specific choices (am=2, γ=0.1, k2=5) are not derived from the paper. The paper focuses on general principles and time-scale separation, not detailed tuning rules. | 0.95 | passed | passed | 0.85 | 0.8 | The paper discusses closed-loop reference model MRAC (CRM-MRAC) and its connection to synchronisation. The answer correctly applies CRM-MRAC to a first-order system, designs a coupling input v = -k2 e, and specifies the reference model. The paper mentions that CRM-MRAC adds a tracking error feedback term to the referen... | The paper introduces the synchronisation-oriented design approach, viewing model-referenced adaptation as synchronisation between actual and virtual dynamic systems. It states: 'The synchronisation-oriented approach consists in the design of a coupling input to achieve desired closed-loop error dynamics followed by the... | arxiv-only | [
"The answer invents specific numerical values (am=2, γ=0.1, k2=5) not present in the paper.",
"The error dynamics de/dt = -(am + k2)e is not derived from the paper; the paper does not provide such explicit closed-loop error dynamics.",
"The adaptive law dθ/dt = γ e x is standard MRAC, not specifically from the ... | [
"The answer's adaptive law (dθ/dt = γ e x) is a standard MRAC law but is not explicitly derived or justified within the synchronisation-oriented framework presented in the paper excerpt. The paper focuses on the design of the coupling input and input allocation, not the specific adaptation law.",
"The answer does... | null | null | null | null | null | [
"The paper does not provide specific tuning guidelines for am, γ, or k2; the chosen values are reasonable but not directly from the paper.",
"The adaptive law dθ/dt = γ e x is standard MRAC but not explicitly derived from the synchronisation perspective in the paper; however, it is consistent with the overall app... |
CS-EVO-00047 | C | L3 | [
"nonlinear",
"robust"
] | 考虑一个由两个子系统通过非线性增益连接构成的互联系统，每个子系统本身是固定时间输入到状态稳定（FxT-ISS）的。若其中一个子系统的Lyapunov函数中描述其FxT-ISS性质的参数α（用于界定系统状态随时间衰减的速率）增大，而其他条件（包括非线性小增益条件）保持不变，那么原论文中提出的Lyapunov小增益定理所保证的整个互联系统的FxT-ISS性质是否仍然成立？为什么？ | 基准条件：系统由两个FxT-ISS子系统互联构成，满足论文中提出的非线性小增益条件。该条件通常涉及子系统Lyapunov函数衰减率参数（如α₁, α₂）和非线性增益函数（如γ₁₂, γ₂₁）满足γ₁₂∘γ₂₁ < id 或类似的不等式。假设变化前参数α₁=1.2，α₂=1.0，增益函数满足小增益条件。变化条件：增大其中一个子系统的衰减率参数α₁至α₁' = 1.5，其他参数和增益函数不变。多方案对比：1) 若α₁增大导致子系统衰减更快，但小增益条件可能更易满足或更难满足，需重新验证不等式。例如，若小增益条件为γ₁₂∘γ₂₁ < id且γ₁₂与α₁相关（如γ₁₂(x)=x^{α₂/α₁}），则α₁增大会改变γ₁₂的形态，可能破坏原有不... | [
"第一步：确认基准系统满足论文中的Lyapunov小增益定理条件，即每个子系统有FxT-ISS Lyapunov函数且整体满足非线性小增益条件。",
"第二步：明确参数α是描述子系统FxT-ISS衰减率的关键参数，其变化可能影响Lyapunov函数导数中的衰减项。",
"第三步：分析参数α增大如何影响子系统Lyapunov函数的衰减速率（通常α越大，衰减越快），以及如何可能影响子系统间的非线性增益函数（因为增益函数常依赖于子系统的稳定性参数）。",
"第四步：推断小增益条件（如γ₁₂∘γ₂₁ < id）可能因α的变化而不再成立，因为增益函数γ的形态或大小可能改变。",
"第五步：得出结论：原FxT-ISS结论... | 2512.21314 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2512.21314",
"title": "Lyapunov Small Gain Fixed Time ISS",
"authors": [],
"year": null,
"paper_path": "2512.21314_Lyapunov_Small_Gain_Fixed_Time_ISS",
"text_offset": 0
} | 该题考察对互联系统固定时间稳定性中小增益条件参数敏感性的理解，要求基于数学结构进行深层推理，满分标准为能清晰阐述参数变化对小增益条件及整体稳定性的影响，并进行多方案对比。 | [
"未明确说明小增益条件的具体数学形式或依赖关系",
"未能对比参数增大和减小两种不同变化方向的影响",
"工程结论模糊，未给出明确的敏感性判定或建议"
] | passed | The paper does not provide explicit formulas linking the FxT-ISS Lyapunov function parameters (α) to the nonlinear gains in the small-gain condition. The small-gain condition is stated in a general nonlinear form (e.g., γ₁₂∘γ₂₁ < id) without specifying dependence on α. The answer invents a specific relationship (γ₁₂(x)... | 0.95 | passed | rejected | 0.9 | 0.9 | The paper introduces a Lyapunov-based small-gain theorem for FxT-ISS interconnected systems, requiring a nonlinear small-gain condition. The answer correctly states that changing a subsystem's Lyapunov parameter α may affect the small-gain condition and that the FxT-ISS property is not guaranteed to hold without re-ver... | The paper's abstract and Section I.C state the main contribution is a Lyapunov-based small-gain theorem for FxT-ISS interconnected systems, where the small-gain condition is a key requirement. The paper does not specify that the small-gain condition involves parameters like α₁, α₂ or functions like γ₁₂(x)=x^{α₂/α₁}. Th... | arxiv-only | [
"The answer assumes a specific functional form for the gain γ₁₂ in terms of α, which is not given in the paper.",
"The paper does not discuss how changes in α affect the small-gain condition; the condition is assumed to be satisfied for the given gains.",
"The answer's conclusion that the FxT-ISS property may b... | [
"Major: The answer invents specific mathematical forms (e.g., γ₁₂(x)=x^{α₂/α₁}) and parameter dependencies (α₁, α₂) that are not defined or discussed in the provided paper excerpt. The paper's small-gain condition is described generally as a 'nonlinear small-gain condition' without specifying its exact form in the ... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | passed | 0.85 | The paper establishes a Lyapunov-based small-gain theorem where the overall FxT-ISS property depends on a '[withheld: verbatim source excerpt]'Domain knowledge beyond the paper excerpt'. The specific formula serves as an illustrative example of how parameters might couple, which is acceptable under the 'creative synthe... | [
"Minor: The specific functional form $\\gamma_{12}(x)=x^{\\alpha_2/\\alpha_1}$ is hypothetical and not derived from the provided text, but it serves as a valid pedagogical example of parameter dependence."
] | [
"The answer provides a specific numerical example (α₁=1.2, α₂=1.0) and a gain formula (γ₁₂(x)=x^{α₂/α₁}) that are not present in the paper excerpt; however, these are reasonable domain knowledge extensions and do not contradict the paper."
] |
CS-EVO-00048 | D | L2 | [
"optimal",
"modern"
] | 针对文献中描述的网络-物理电力系统（CPPS）在遭受网络攻击时的弹性运行问题，请设计一个完整的协同控制方案，以实现以下控制目标：在网络通信链路被部分切断的攻击场景下，通过协调激活备用通信链路（网络层动作）和调度储能系统（物理层动作），共同最小化系统总运行成本（包括发电成本和网络重构成本），并恢复关键负荷的供电。工程约束为：网络拓扑重构需在5秒内完成，储能系统的有功功率调节速率不低于5 MW/s，且关键负荷的供电恢复需在60秒内实现。 | 1. **系统建模**：建立CPPS的混合整数二阶锥规划（MISOCP）模型。物理层为ACOPF模型：\[ \min \sum_{i\in\mathcal{G}} c_i P_{gi} + \sum_{e\in\mathcal{E}} \gamma_e s_e \]，满足潮流方程（AC功率平衡）、电压幅值上下限\(V_{i}^{\min} \leq V_i \leq V_{i}^{\max}\)、线路容量约束以及储能系统（ESS）充放电约束\(P_{\text{ESS},t} = P_{\text{ESS},t-1} + \eta P_{\text{ch},t} - P_{\text{dis},t}/\eta\)，其中\(P_{\t... | [
"问题要求设计一个针对CPPS的协同控制方案，以在网络攻击下最小化运行成本并恢复负荷。",
"控制目标明确：协调网络重构（激活通信链路）和物理控制（调度储能）。工程约束给定：网络重构时间5秒，储能调节速率5 MW/s，负荷恢复时间60秒。",
"系统建模需涵盖物理层ACOPF和网络层拓扑约束，目标函数包含两种成本。采用MISOCP模型可处理物理层非凸约束。",
"控制器选型需考虑双层结构以解耦网络和物理层，上层用MILP解决离散的网络重构，下层用MPC实现在线物理控制，符合时间尺度差异。",
"参数整定需依据约束设定：网络层时限5秒，MPC预测时域对应60秒，ESS速率离散化为约束。权重需突出负荷恢复重要性。... | 2502.05768 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在给定约束下数学和工程上是否可行，如模型、约束和参数是否合理。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择（双层优化、MPC）是否恰当，理由是否充分，是否针对CPPS协同优化的特点。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"descr... | needs_review | {
"arxiv_id": "2502.05768",
"title": "Cooperative Optimization of Grid Edge Cyber and Physical Res",
"authors": [],
"year": null,
"paper_path": "2502.05768_Cooperative_Optimization_of_Grid_Edge_Cyber_and_Physical_Res",
"text_offset": 0
} | 该题考察被测试者针对网络-物理电力系统弹性运行问题，设计完整协同控制方案的能力，包括混合系统建模、双层优化与MPC控制器设计、参数整定、性能分析和工程约束考量，满分要求方案完整、参数具体、分析全面、工程可行。 | [
"建模部分未完整包含物理层和网络层的目标函数与约束，或数学表达式错误。",
"控制器选型理由不充分，未清晰说明为何选择双层优化和MPC。",
"参数整定部分未给出具体的参数数值（如MPC的预测时域、权重系数）或整定过程。",
"性能验证未分析稳定性、响应时间和稳态误差，或分析过于笼统。"
] | passed | The paper does not propose a specific control scheme with MISOCP, MPC, or detailed parameter tuning. It presents a bi-level optimization framework for cyber topology reconfiguration and physical resource control, but the answer introduces many details (e.g., MISOCP, MPC, specific time constraints, ESS dynamics) that ar... | 0.95 | passed | passed | 0.9 | 0.8 | The paper proposes a bi-level optimization framework for cooperative cyber-physical resource optimization, including cyber topology reconfiguration and physical resource control (e.g., energy storage). The answer's use of MISOCP, MILP, MPC, and the bi-level structure aligns with the paper's approach. The paper mentions... | The paper's abstract and Section I describe a bi-level solution for cooperative cyber-physical resource optimization, including reconfiguration of cyber topology (activation of communication links) and control of physical resources (e.g., energy storage systems) to improve grid resilience. The answer's proposed bi-leve... | arxiv-only | [
"The paper does not mention MISOCP or MPC; it uses a bi-level optimization with ACOPF and binary cyber variables.",
"The answer specifies time constraints (5s, 60s) and ESS rate limits (5 MW/s) that are not in the paper.",
"The answer's parameter tuning (e.g., N_p=6, T_s=10s) is not derived from the paper.",
... | [
"The answer introduces specific technical details (MISOCP, MPC, parameter values like Np=6, Ts=10s) not present in the provided paper excerpt. This is acceptable as domain knowledge synthesis, but the confidence is reduced because the paper excerpt does not detail the specific optimization formulations or control m... | null | null | null | null | null | null |
CS-EVO-00049 | C | L2 | [
"optimal",
"robust"
] | 在基于控制屏障函数（CBF）的CAV最优控制框架中，考虑事件触发机制下的二次规划（QP）可行性。若将CBF约束中的安全裕度参数ε（定义保证安全状态区域边界的松弛量）从基准值减小，分析此变化对QP可行域大小及系统安全保证的影响。 | 1. 基准条件复述：在OCBF框架中，安全约束通过CBF表达为 h(x) ≥ 0。为处理实时不确定性，引入安全裕度参数ε > 0，使得实际约束为 h(x) ≥ ε。基准条件设定ε为一个固定正数，以确保安全区域的内部点满足约束。2. 变化条件分析：将ε从基准值ε₀减小至ε₁（ε₁ < ε₀）。量化变化：安全区域边界从h(x) ≥ ε₀放宽至h(x) ≥ ε₁，即允许状态更接近原始安全边界h(x) = 0。3. 多方案对比：- 方案A（ε减小）：安全裕度减小，CBF约束h(x) ≥ ε变得更容易满足。这导致QP的可行域扩大，因为在每个离散时间步，更多的控制输入能满足约束。然而，系统状态被允许更接近不安全区域，安全保证的“缓冲”减小。- ... | [
"CBF安全约束通常表达为 h(x) ≥ 0，其中h(x)为连续可微函数。",
"引入安全裕度ε后，实际约束变为 h(x) ≥ ε，以处理离散时间步间的状态演化。",
"将ε从基准值ε₀减小到ε₁（ε₁ < ε₀），直接使不等式右端减小。",
"对于固定的状态x，若原来满足 h(x) ≥ ε₀，则必然满足 h(x) ≥ ε₁，因此满足约束的状态集合（可行域）扩大。",
"可行域扩大意味着在线求解QP时，存在更多满足约束的控制解，降低了不可行风险。",
"然而，h(x) ≥ ε₁ 允许状态更接近 h(x)=0 的危险边界，安全裕量减小。"
] | 2209.13053 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2209.13053",
"title": "Optimal Control of Connected Automated Vehicles with EventSe",
"authors": [],
"year": null,
"paper_path": "2209.13053_Optimal_Control_of_Connected_Automated_Vehicles_with_EventSe",
"text_offset": 0
} | 考察在CBF约束中改变安全裕度参数ε时，对QP可行域和系统安全保证的敏感性分析，需进行量化对比和工程结论。 | [
"未明确量化ε变化前后的数值对比（如 ε₀=0.1, ε₁=0.05）。",
"未对比至少两种不同的参数变化方向（如仅分析减小，未提及增大的影响）。",
"工程结论未给出明确的敏感性判定或建议。"
] | passed | The paper does not discuss a safety margin parameter ε in the CBF constraints. The OCBF framework uses CBFs to enforce constraints, but no such parameter ε is mentioned. The paper focuses on event-triggered and self-triggered approaches to ensure QP feasibility, not on adjusting a safety margin. | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses CBF-based constraints and QP feasibility, and the concept of safety margins is consistent with the CBF framework. The answer's analysis of reducing ε expanding the feasible region and reducing safety buffer aligns with standard CBF theory, though the paper does not explicitly define ε as a safety ma... | The paper states: 'CBFs can be used with nonlinear (affine in control) system dynamics and they have a crucial forward invariance property which guarantees the satisfaction of safety constraints over all time as long as these constraints are initially satisfied.' The answer's discussion of safety constraints h(x) ≥ ε a... | arxiv-only | [
"The concept of a safety margin parameter ε in CBF constraints is not present in the paper.",
"The analysis of changing ε and its effect on QP feasibility and safety is not supported by the paper.",
"The paper does not discuss engineering recommendations about adjusting ε."
] | [
"Minor: The paper does not explicitly define or discuss a safety margin parameter ε in the provided excerpt. The answer introduces this parameter as part of a reasonable engineering analysis, which is acceptable domain knowledge but not directly sourced from the paper."
] | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | [
"The paper does not explicitly introduce a parameter ε as a safety margin; the answer assumes a common practice in CBF literature."
] |
CS-EVO-00050 | A | L1 | [
"classical"
] | 在输入饱和不确定线性系统的鲁棒控制综合中，什么是死区非线性的静态扇形条件？ | 死区非线性的静态扇形条件是指，对于输入饱和非线性，可以将其等效为一个死区非线性。该条件要求死区非线性函数 φ(u) 满足：φ(u) 属于扇形区域 [0, I]，即对于所有输入 u，满足 0 ≤ u^T φ(u) ≤ u^T u。该条件提供了对饱和非线性的一种保守但易于处理的近似，常用于绝对稳定性分析。 | [
"输入饱和非线性可以建模为一个死区非线性。",
"静态扇形条件是对该死区非线性施加的特定约束。",
"该约束具体表述为不等式 0 ≤ u^T φ(u) ≤ u^T u，其中 φ(u) 是死区输出，u 是控制器输出。"
] | 2603.07907 | mimo | null | null | null | needs_review | {
"arxiv_id": "2603.07907",
"title": "Robust control synthesis for uncertain linear systems with i",
"authors": [],
"year": null,
"paper_path": "2603.07907_Robust_control_synthesis_for_uncertain_linear_systems_with_i",
"text_offset": 0
} | 该题考察对输入饱和建模中经典静态扇形条件这一核心概念定义的精确回忆。满分标准为能准确写出该条件的数学不等式并说明其适用对象。 | [
"漏写不等式的任一部分（如 0 或 u^T u）。",
"未明确说明该条件是针对死区非线性。",
"将扇形条件错误地关联到其他非线性（如Popov准则）。"
] | passed | The paper does not explicitly define the static sector condition for dead-zone nonlinearity. It mentions 'conventional approaches based on a single static sector condition for the dead-zone nonlinearity' in the abstract and introduction, but does not provide the specific inequality 0 ≤ u^T φ(u) ≤ u^T u. The answer appe... | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses input saturation and dead-zone nonlinearity, and mentions 'static sector condition' in the context of IQC-based methods. The answer correctly describes the static sector condition for dead-zone nonlinearity as φ(u) ∈ [0, I], which is standard in the literature and consistent with the paper's approac... | The paper states: 'Compared with conventional approaches based on a single static sector condition for the dead-zone nonlinearity, the proposed method yields improved L2-gain performance...' This confirms that a static sector condition for the dead-zone nonlinearity is a conventional approach used in the field. The ans... | arxiv-only | [
"The answer provides a definition not found in the source paper; the paper only references the existence of such a condition without stating it explicitly."
] | [
"Minor: The answer provides a specific mathematical formulation (0 ≤ u^T φ(u) ≤ u^T u) that is not explicitly quoted in the provided excerpt, but it is a standard and correct representation of the static sector condition [0, I] for a dead-zone nonlinearity in control literature, and does not contradict the paper."
... | [
"A维答案过于模糊：缺少 LaTeX 公式、条件-结论结构、或 ≥3 个控制科学术语",
" - 未检测到 LaTeX 公式标记",
" - 未检测到条件-结论结构",
" - 控制科学术语不足（仅 2/3）"
] | null | null | null | null | null |
CS-EVO-00051 | B | L3 | [
"modern",
"classical"
] | 给定一个连续时间线性系统的状态方程 ẋ = Ax + Bu，其中 A = [[0, 1], [-5, -2]]，B = [[0], [1]]。首先，通过计算系统矩阵A的特征值来判断其稳定性。然后，若采用状态反馈 u = -Kx，其中 K = [k1, k2]，欲使闭环系统矩阵 A - BK 的特征值均位于左半开平面（稳定），请推导增益k1和k2必须满足的条件（即稳定区域）。 | 系统矩阵 A 的特征多项式为 det(sI - A) = s² + 2s + 5。特征值为 s = -1 ± 2j，实部为负，故开环系统稳定。闭环系统矩阵 A - BK = [[0, 1], [-5 - k1, -2 - k2]]。其特征多项式为 s² + (2 + k2)s + (5 + k1)。根据Routh-Hurwitz判据，对于二阶系统，闭环稳定的充要条件是所有系数均为正：1 > 0，2 + k2 > 0，5 + k1 > 0。因此，增益必须满足 k1 > -5 且 k2 > -2。 | [
"计算开环系统矩阵A的特征多项式 det(sI - A) = s² + 2s + 5，特征值为 -1 ± 2j，实部为负，故开环系统稳定。",
"写出闭环系统矩阵 A - BK = [[0, 1], [-5 - k1, -2 - k2]]，并计算其特征多项式为 s² + (2 + k2)s + (5 + k1)。",
"对二阶系统应用Routh-Hurwitz判据（或直接分析），闭环稳定的充要条件是特征多项式所有系数均为正，得到不等式组 2 + k2 > 0 和 5 + k1 > 0。",
"解不等式组，得出增益k1和k2必须满足的条件为 k1 > -5 且 k2 > -2。"
] | FRC | mimo | null | null | null | needs_review | {
"arxiv_id": "FRC",
"title": "Controls Engineering",
"authors": [],
"year": 2017,
"paper_path": "FRC_Controls_Engineering",
"text_offset": 0
} | 该题考察对连续时间线性系统稳定性的判断以及状态反馈增益设计的稳定性条件推导能力，要求能综合运用特征值分析、状态反馈构建和Routh-Hurwitz判据进行多步推理。 | [
"未正确计算或列出开环系统矩阵A的特征值，导致对开环稳定性的判断错误。",
"在构建闭环矩阵A - BK时符号或代数运算错误。",
"未正确应用Routh-Hurwitz判据或遗漏稳定性条件（如要求所有系数为正）。",
"最终推导出的增益条件不完整或存在符号错误。"
] | passed | The source paper does not contain the specific example or derivation of stability conditions for the given A and B matrices. The paper covers state-space control and pole placement in general, but the answer's calculations are not directly supported by any passage. | 1 | passed | passed | 0.95 | 0.95 | The paper covers state-space control, pole placement, and stability via eigenvalues (Sections 6.4, 7.6). The answer correctly computes eigenvalues, forms the closed-loop matrix, derives the characteristic polynomial, and applies the Routh-Hurwitz condition for a second-order system. The paper does not explicitly discus... | The paper covers continuous state-space control (Chapter 6), eigenvalues and stability (Section 6.4), and closed-loop controller design (Section 6.5). The answer correctly applies standard control theory concepts (characteristic polynomial, Routh-Hurwitz criterion) that are consistent with the paper's domain. The paper... | textbook-unchecked | [
"The answer's derivation is mathematically correct but not supported by the source paper.",
"The paper does not provide the specific A and B matrices or the resulting stability conditions."
] | null | null | null | null | null | null | null |
CS-EVO-00052 | D | L4 | [
"multi_agent",
"robust",
"modern"
] | 针对具有矩阵加权符号网络的线性多智能体系统，请设计一个基于公平分区的分布式观测器，以实现对整个系统状态的渐近观测，并满足以下工程约束：观测器对模型不确定性的鲁棒性增益不低于10 dB，状态估计误差收敛时间小于2秒。 | 1. 系统建模：考虑具有矩阵加权符号网络的N个智能体线性系统，其动力学为 \( \dot{x}_i = A x_i + B u_i \)，通信拓扑由拉普拉斯矩阵L描述，L的元素为矩阵权重。系统状态为 \( X = [x_1^T, ..., x_N^T]^T \)，整体动态为 \( \dot{X} = (I_N \otimes A + L \otimes B K) X \)。2. 控制器选型：选择分布式观测器 \( \dot{\hat{X}} = (I_N \otimes A + L \otimes B K) \hat{X} + \Gamma (Y - \hat{Y}) \)，其中 \( \hat{X} \) 为估计状态，\( Y \... | [
"建立具有矩阵加权符号网络的线性多智能体系统状态空间模型，明确整体动态方程。",
"提出一个分布式观测器结构，该结构利用公平分区信息和网络拓扑进行状态估计。",
"基于公平分区理论选择观测器增益矩阵的形式，并说明其分布式和结构性优势。",
"给出观测器增益参数的具体整定方法，包括基于收敛时间要求的特征值配置和基于鲁棒性要求的频域条件。",
"分析所设计观测器的关键性能指标，包括稳定裕度、响应时间和稳态误差，并验证其满足给定工程约束。",
"讨论实际工程实施中可能遇到的通信、计算和模型不确定性等约束及注意事项。"
] | 2204.00995 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否针对给定系统（矩阵加权符号网络MAS）和工程约束（鲁棒性增益、收敛时间）可行，建模和观测器结构是否合理。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择分布式观测器并基于公平分区是否恰当，选择理由是否充分说明了方法与问题特性的匹配度。"
},
"completeness": {
"max_score": 1,
"we... | needs_review | {
"arxiv_id": "2204.00995",
"title": "Controllability and observability of linear multi agent syst",
"authors": [],
"year": null,
"paper_path": "2204.00995_Controllability_and_observability_of_linear_multi_agent_syst",
"text_offset": 0
} | 本题考察针对矩阵加权符号网络多智能体系统设计分布式观测器的完整控制方案能力，满分标准为方案包含系统建模、选型理由、参数整定、性能验证和工程考量五部分，且数学表达完整、约束满足。 | [
"系统建模部分未正确写出整体动态方程或遗漏矩阵权重/符号特性。",
"控制器选型未说明与公平分区或网络结构的关联性。",
"参数整定部分未给出满足鲁棒性增益（10dB）和收敛时间（<2s）的具体条件或计算过程。",
"性能验证未涵盖稳定裕度、响应时间、稳态误差等关键指标，或指标分析错误。"
] | passed | The paper does not discuss observer design, robustness, convergence time, or any engineering constraints such as gain margins or settling time. It focuses on controllability and observability analysis using equitable partitions, not on constructing observers. | 1 | passed | rejected | 0.3 | 0.9 | The paper discusses equitable partitions for controllability/observability analysis of matrix-weighted signed networks, but does not provide any design procedure for distributed observers, robustness specifications, or convergence time constraints. The answer invokes concepts from the paper (equitable partition, matrix... | The paper's abstract and introduction focus on analyzing controllability and observability of linear multi-agent systems over matrix-weighted signed networks, using equitable partitions to derive bounds and conditions. It does not propose or design a specific distributed observer. The answer constructs a detailed obser... | redistributable | [
"The answer invents a distributed observer design not present in the paper.",
"The answer specifies numerical performance requirements (10 dB, 2 seconds) not mentioned in the paper.",
"The paper does not provide any LMI conditions or gain tuning methods.",
"The answer misapplies concepts like 'fair partition'... | [
"The answer is a creative engineering design that goes far beyond the paper's scope, which is theoretical analysis (controllability/observability conditions) rather than observer synthesis.",
"The answer introduces specific performance constraints (10 dB, 2s) and design steps (LMI, gain tuning) not discussed in t... | null | passed | 0.95 | The question explicitly asks to 'design' (设计) a distributed observer based on the concepts in the paper, subject to specific engineering constraints. This is a Design/Synthesis question (Dimension D), not a factual retrieval question. The source paper provides the theoretical foundation (matrix-weighted signed networks... | [
"Minor: The answer assumes a specific form for the output matrix Y and the coupling term which are not explicitly defined in the excerpt, but this is necessary for the design task.",
"Note: The specific numerical constraints (10 dB, 2s) are arbitrary inputs from the user, not derived from the paper, which is appr... | [
"The answer proposes a specific observer structure and tuning method not present in the paper.",
"Robustness gain of 10 dB and convergence time <2s are arbitrary engineering constraints not mentioned in the paper.",
"The paper focuses on controllability/observability analysis, not observer design."
] |
CS-EVO-00053 | C | L4 | [
"nonlinear",
"robust"
] | 在数据驱动收缩控制框架中，若假设的多项式动力学非线性度（Lipschitz常数）增大，原基于黎曼度量的收缩性判据是否仍然成立？请基于基准条件（假设非线性满足Lipschitz常数L₀=2的多项式动力学）进行分析，并比较L增大至L₁=5和减小至L₂=1时的结论。 | 基准条件：原系统为多项式动力学，非线性满足Lipschitz常数L₀=2，且存在一个状态相关的黎曼收缩度量M(x)使得δxᵀM(x)δx沿系统轨迹的导数负定，从而保证数据驱动闭环收缩性。
变化条件分析：若Lipschitz常数从L₀=2增大至L₁=5，意味着非线性更强，轨迹发散趋势增加，原收缩度量M(x)可能不足以保证δxᵀM(x)δx的导数在整个状态空间上保持负定，收缩性判据可能失效。若L减小至L₂=1，非线性减弱，轨迹收敛趋势增强，原收缩度量M(x)或更小的度量仍可能满足判据，收缩性更容易保持。
多方案对比：1) L增大（L₁=5）：收缩性判据可能被破坏，需重新搜索或验证度量M(x)，计算复杂度增加。2) L减小（L₂=1）：收... | [
"步骤1：基准条件中，多项式动力学的非线性由Lipschitz常数L₀=2表征，且存在黎曼度量M(x)满足收缩性判据。",
"步骤2：当Lipschitz常数增大至L₁=5时，非线性增强，可能使δxᵀM(x)δx的导数不再负定，破坏收缩性条件。",
"步骤3：当Lipschitz常数减小至L₂=1时，非线性减弱，原度量M(x)可能仍然满足收缩性判据，或可用更简单的度量替代。",
"步骤4：对比两种变化，L增大导致判据失效风险高，L减小则判据更可能保持，表明判据对L敏感。"
] | 2412.20283 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2412.20283",
"title": "Convex Data Driven Contraction With Riemannian Metrics",
"authors": [],
"year": null,
"paper_path": "2412.20283_Convex_Data_Driven_Contraction_With_Riemannian_Metrics",
"text_offset": 0
} | 考察在数据驱动收缩控制中，非线性度（Lipschitz常数）变化对收缩性判据的影响，要求量化分析并多方案对比，满分标准为完整分析敏感性、对比不同变化方向并给出工程结论。 | [
"未明确基准条件的数值（L₀=2）",
"未量化对比L增大和减小的具体影响",
"工程结论未提及对数据驱动控制设计的建议",
"数学表达式（如δxᵀM(x)δx）未完整呈现"
] | rejected | The paper does not discuss Lipschitz constants or their variation. It focuses on polynomial dynamics and Riemannian metrics, with no mention of Lipschitz bounds or sensitivity analysis. The answer invokes concepts (Lipschitz constant L₀=2, L₁=5, L₂=1) that are absent from the source paper. | 0.95 | passed | rejected | 0.9 | 0.9 | The paper discusses contraction under Riemannian metrics for polynomial dynamics, and the answer's reasoning about Lipschitz constants affecting contraction is consistent with the general concept that stronger nonlinearities can break contraction. The paper does not explicitly analyze varying Lipschitz constants, but t... | The paper's abstract and introduction state that the work extends analysis to 'polynomial dynamics' and uses 'Riemannian metrics' for contraction. However, the paper does not discuss Lipschitz constants or their role in the contraction criteria. The paper's core contribution is a convex data-driven formulation for find... | redistributable | [
"The paper does not assume Lipschitz bounded nonlinearities; it assumes polynomial dynamics.",
"No Lipschitz constants are mentioned or analyzed in the paper.",
"The answer's analysis of varying Lipschitz constants is not supported by the paper.",
"The paper's contraction criteria are based on convex conditio... | [
"The answer is based on a premise (Lipschitz constant sensitivity analysis) that is not discussed or supported by the provided paper excerpt. The paper focuses on polynomial dynamics and Riemannian metrics, not on Lipschitz bounds as a parameter for contraction criteria.",
"The answer's analysis is speculative an... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | rejected | 0.95 | The provided paper excerpt explicitly states in the Abstract that previous work assumed 'nonlinearities are Lipschitz bounded', but this paper extends the analysis by 'considering Riemannian metrics for polynomial dynamics'. The Introduction further clarifies that the proposed method avoids the conservatism of bounding... | [
"The answer relies on a Lipschitz constant sensitivity analysis framework that is explicitly contrasted with the paper's approach in the Abstract.",
"The specific values (L=2, 5, 1) are hallucinated and have no basis in the source text.",
"The paper focuses on polynomial dynamics where global Lipschitz constant... | null |
CS-EVO-00055 | B | L2 | [
"classical"
] | 给定一个连续时间线性系统，其状态空间描述为：
ẋ = A x + B u, 其中 A = [[0, 1], [-a, -b]], B = [[0], [1]]，a=4, b=5。设计一个状态反馈控制律 u = -K x，K = [k1, k2]，使得闭环系统矩阵 A_cl = A - B K 的特征值均为 -2 ± j2。求出反馈增益矩阵 K。 | 闭环系统矩阵 A_cl = A - B K = [[0, 1], [-a - k1, -b - k2]]。特征多项式为 det(λI - A_cl) = λ² + (b + k2) λ + (a + k1)。期望特征值为 λ = -2 ± j2，对应的特征多项式为 (λ + 2 - j2)(λ + 2 + j2) = λ² + 4λ + 8。比较系数得：b + k2 = 4, a + k1 = 8。代入 a=4, b=5，解得 k1 = 4, k2 = -1。因此 K = [4, -1]。 | [
"写出状态反馈控制下的闭环系统矩阵 A_cl = A - B K。",
"计算 A_cl 的特征多项式 det(λI - A_cl) = λ² + (b + k2) λ + (a + k1)。",
"根据期望特征值 -2 ± j2 写出目标特征多项式 λ² + 4λ + 8。",
"令两个多项式系数相等，得到方程组 b + k2 = 4 和 a + k1 = 8。",
"代入已知数值 a=4, b=5，求解得 k1=4, k2=-1。",
"得出反馈增益矩阵 K = [k1, k2] = [4, -1]。"
] | 2207.08730 | mimo | null | null | null | needs_review | {
"arxiv_id": "2207.08730",
"title": "A framework for online stabilizing reinforcement learning",
"authors": [],
"year": null,
"paper_path": "2207.08730_A_framework_for_online_stabilizing_reinforcement_learning",
"text_offset": 0
} | 该题考察基于极点配置的状态反馈控制器设计，需要多步代数推导和系数匹配，符合B维度多步推理链要求。 | [
"未正确写出闭环系统矩阵或特征多项式。",
"期望特征多项式推导错误。",
"系数匹配方程建立错误。",
"代入数值后求解计算出错。"
] | passed | The source paper does not contain any linear system pole placement examples or the specific matrices and equations used in the question and answer. The paper focuses on Lyapunov-based stabilizing reinforcement learning for nonlinear systems, not on classical control design for linear systems. | 1 | passed | passed | 0.95 | 0.95 | The paper discusses Lyapunov-based stabilizing reinforcement learning and mentions state feedback control, but does not contain specific linear system pole placement examples. The answer is a standard control theory calculation that does not contradict any content in the paper. | The paper discusses Lyapunov-based stabilizing reinforcement learning and classical control concepts, but does not contain the specific linear system or pole placement problem presented in the question. The answer correctly applies standard control theory (pole placement via state feedback) which is consistent with the... | arxiv-only | [
"The answer is a standard control theory calculation unrelated to the paper's content.",
"The paper does not provide the system matrices A, B or the desired eigenvalues.",
"The answer cannot be verified against the source paper."
] | null | null | null | null | null | null | null |
CS-EVO-00057 | D | L4 | [
"nonlinear",
"robust"
] | 针对文献中提出的带有正参数a的事件触发控制算法，设计一个具体的控制器参数整定方案，使得闭环系统稳定且能排除Zeno行为。请给出完整的控制方案，包括建模、选型、参数整定、性能验证和工程考量。 | 1. 系统建模：考虑非线性时滞系统模型(1)，其中状态x∈ℝⁿ，控制律u(t)=k(x(tᵢ))。事件触发条件为‖e(t)‖ ≤ ae^{-b(t-t₀)}‖x(t)‖，其中e(t)=x(tᵢ)-x(t)，a>0, b>0为可调参数。2. 控制器选型：采用事件触发状态反馈控制，原因在于其能减少通信和计算资源，同时通过设计合适的a和b保证稳定性并避免Zeno行为。3. 参数整定：选择a和b的值，满足文献中定理2（或3）的充分条件。例如，取a=0.1, b=1，需验证其满足稳定性判据（如基于Lyapunov-Krasovskii泛函的条件）。4. 性能验证：分析稳定性（利用Halanay不等式证明状态最终有界且吸引）、响应时间（由触发间... | [
"基于文献模型(1)建立事件触发控制系统的数学模型。",
"选择事件触发状态反馈控制方法，理由是其资源高效性与稳定性保证。",
"依据文献定理的充分条件整定参数a和b，并给出具体数值示例。",
"通过Halanay不等式和触发间隔分析验证稳定性、响应时间和稳态误差性能。",
"讨论工程实施中参数权衡、硬件要求等约束和注意事项。"
] | 2207.03566 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否基于文献模型，参数整定是否符合稳定性条件，工程约束是否合理。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型是否适合事件触发控制场景，理由是否充分。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否涵盖建模、选... | needs_review | {
"arxiv_id": "2207.03566",
"title": "A Note on Stability of Event Triggered Control Systems with",
"authors": [],
"year": 2020,
"paper_path": "2207.03566_A_Note_on_Stability_of_Event_Triggered_Control_Systems_with",
"text_offset": 0
} | 该题考察设计完整事件触发控制方案的能力，包括从建模到工程落地的全流程，Judge满分标准为方案完整、参数有据、性能分析到位、工程考量全面。 | [
"数学模型未完整引用文献中的系统方程(1)或触发条件。",
"参数整定过程未明确引用文献中的定理条件或合理性说明。",
"性能验证部分缺失稳定性、Zeno行为排除或误差分析中的任一关键点。",
"工程考量过于笼统，未涉及具体约束（如时滞、通信限制）或参数权衡。"
] | passed | The paper does not provide a specific parameter tuning scheme; it only proves that stability holds under the conditions of Theorem 2/3 from [1] and that b can be arbitrarily chosen to exclude Zeno behavior. The answer invents specific values (a=0.1, b=1) and a tuning procedure not present in the paper. | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses event-triggered control for nonlinear time-delay systems with triggering condition ‖e(t)‖ ≤ a e^{-b(t-t₀)}‖x(t)‖, and shows that positive a can be used while ensuring stability and excluding Zeno behavior. The answer correctly references the system model, triggering condition, and the use of Halanay... | The paper states: 'In the designed event-triggering condition, the exponential function $a e ^ { - b ( t - t _ { 0 } ) }$ with tunable parameters a and b plays a vital role in ensuring boundedness and attractivity of the system states while excluding Zeno behavior.' The answer correctly identifies the event-triggering ... | arxiv-only | [
"The answer proposes a concrete parameter tuning scheme (e.g., a=0.1, b=1) which is not given in the paper.",
"The paper does not provide a step-by-step controller design procedure; it only analyzes stability and Zeno exclusion.",
"The answer mentions 'Lyapunov-Krasovskii functional' but the paper uses a Halana... | [
"Minor: The answer's event-triggering condition is given as ‖e(t)‖ ≤ ae^{-b(t-t₀)}‖x(t)‖, but the paper excerpt does not explicitly state this exact form; it only references the exponential function ae^{-b(t-t₀)}. However, this is a standard form in event-triggered control and is consistent with the paper's descrip... | null | null | null | null | null | null |
CS-EVO-00058 | C | L3 | [
"multi_agent",
"robust"
] | 在论文提出的分布式控制律下，若将系统参数λ（与图拉普拉斯矩阵相关的增益）从基准值λ₀减小到0.5λ₀，同时保持其他条件（如噪声强度σ、性能函数参数ρ、期望收敛速度）不变，分析这对随机多智能体系统实现“q阶矩期望一致性”的可行性有何影响？ | 基准条件：系统具有N个智能体，通信拓扑图拉普拉斯矩阵L，控制律u_i(t) = -λ(t)∑_{j∈N_i} a_{ij}(x_i(t)-x_j(t)) + v_i(t)，其中λ(t)为时变增益，v_i(t)为外部控制输入。性能约束为|e_i(t)| ≤ ρ(t) = (ρ_0 - ρ_∞)e^{-kt} + ρ_∞，其中ρ_0, ρ_∞, k > 0为预定义参数。系统动态为dx_i(t) = [f(x_i(t)) + u_i(t)]dt + g(x_i(t))dW_i(t)，噪声强度σ与g(x_i(t))相关。基准增益为λ₀，满足论文中条件(13)和(18)以确保q阶矩期望一致性。变化条件：将增益λ₀减小至λ₁ = 0.5λ₀。多... | [
"识别论文中控制律的关键参数λ及其在条件(13)和(18)中的作用。",
"分析λ减小对Lyapunov稳定性条件V̇ < 0的影响，具体到误差动力学e(t)的收敛性。",
"对比λ减小与λ增大两种情况下，系统是否能同时满足q阶矩期望一致性和性能约束。",
"得出λ的敏感性判定：λ必须足够大以满足条件，减小λ会破坏一致性。"
] | 2203.03665 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2203.03665",
"title": "Distributed Consensus of Stochastic Multi agent Systems with",
"authors": [],
"year": null,
"paper_path": "2203.03665_Distributed_Consensus_of_Stochastic_Multi_agent_Systems_with",
"text_offset": 0
} | 考察对论文中分布式控制律参数λ的敏感性分析，需结合随机一致性条件和性能约束，评估参数变化对系统可行性的影响。 | [
"未明确引用论文中的具体条件（如(13)或(18)），导致分析缺乏依据。",
"未给出λ变化对性能约束的具体影响，只讨论了一致性。",
"多方案对比不充分，仅分析了λ减小，未提及λ增大或保持不变的对比。",
"工程结论未给出具体参数调整建议，仅定性描述。"
] | passed | The paper does not provide explicit conditions (13) and (18) as referenced in the answer. The answer invokes specific equation numbers and a Lyapunov derivative condition that are not present in the provided source text. The paper discusses sufficient conditions for consensus in expectation and almost sure consensus, b... | 0.95 | passed | rejected | 0.9 | 0.9 | The paper discusses distributed consensus control with prescribed performance constraints, and the answer correctly interprets that reducing the gain λ may violate sufficient conditions (e.g., conditions (13) and (18) mentioned in the paper) for consensus in expectation. The answer's reasoning about Lyapunov analysis a... | The paper's control law is given in equation (1) as u_i(t) = -λ(t)∑_{j∈N_i} a_{ij}(x_i(t)-x_j(t)) + v_i(t). The sufficient conditions for consensus are provided in Theorem 1 (conditions (13) and (18)). Condition (13) involves the minimum eigenvalue of the Laplacian matrix L and the gain λ(t). Specifically, condition (1... | redistributable | [
"The answer references conditions (13) and (18) which do not appear in the provided paper excerpt.",
"The answer assumes a specific Lyapunov derivative condition V̇ < 0 that is not mentioned in the source.",
"The paper does not provide a baseline λ₀ or discuss sensitivity of λ in the context of qth moment conse... | [
"The answer incorrectly specifies the performance constraint function ρ(t) = (ρ_0 - ρ_∞)e^{-kt} + ρ_∞, which is not defined in the provided paper excerpt.",
"The answer's analysis is largely consistent with the paper's concepts but relies on domain knowledge beyond the excerpt, which is acceptable. However, the s... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | passed | 0.95 | The answer correctly identifies the core control-theoretic implication: reducing the control gain $λ$ weakens the stabilizing term in the Lyapunov analysis, potentially violating the sufficient conditions for consensus (which typically require the gain to dominate noise and performance constraint derivatives). Although... | [
"Minor: The specific equation numbers (13, 18) and the exact formula for $ρ(t)$ are inferred from standard PPC literature/domain knowledge rather than being explicitly present in the provided text snippet, but this is acceptable under the 'Domain knowledge beyond the paper excerpt is acceptable' principle."
] | null |
CS-EVO-00059 | B | L3 | [
"classical",
"modern"
] | 假设一个简化的二维磁控微型游泳机器人在粘性流体中的运动模型可以近似为：
\[
\dot{x}(t) = A x(t) + B u(t)
\]
其中状态向量 \(x(t) = [x_1(t), x_2(t)]^T\) 表示机器人在两个正交方向上的位置，控制输入 \(u(t) = [u_1(t), u_2(t)]^T\) 表示施加的磁场分量。已知系统矩阵 \(A = \begin{bmatrix} -1 & 0.5 \\ -0.2 & -0.8 \end{bmatrix}\)，输入矩阵 \(B = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\)。请分析该系统在状态反馈控制 \(u(t) = ... | 首先，写出闭环系统矩阵 \(A_{cl} = A - BK = \begin{bmatrix} -1 - k_{11} & 0.5 - k_{12} \\ -0.2 - k_{21} & -0.8 - k_{22} \end{bmatrix}\)。目标是让闭环系统矩阵的特征值实部小于 -1。考虑将特征值配置到实部为 -2 的位置。尝试选择 \(K = \begin{bmatrix} 1 & 0.5 \\ -0.2 & 0.2 \end{bmatrix}\)。代入得 \(A_{cl} = \begin{bmatrix} -2 & 0 \\ 0 & -1 \end{bmatrix}\)。计算特征值：\(\lambda_1 = -2\)，... | [
"第一步：写出状态反馈控制下的闭环系统矩阵表达式 \\(A_{cl} = A - BK\\)。",
"第二步：将给定的 \\(A\\) 和 \\(B\\) 矩阵代入，得到 \\(A_{cl}\\) 关于 \\(K = \\begin{bmatrix} k_{11} & k_{12} \\\\ k_{21} & k_{22} \\end{bmatrix}\\) 的具体形式。",
"第三步：为满足特征值实部小于 -1 的性能要求，将闭环系统矩阵设计为对角矩阵 \\(\\text{diag}(-2, -1.6)\\)。",
"第四步：建立方程组 \\(A - BK = \\begin{bmatrix} -2 & 0 \... | 2201.05599 | mimo | null | null | null | needs_review | {
"arxiv_id": "2201.05599",
"title": "Smart Magnetic Microrobots Learn to Swim with Deep Reinforce",
"authors": [],
"year": null,
"paper_path": "2201.05599_Smart_Magnetic_Microrobots_Learn_to_Swim_with_Deep_Reinforce",
"text_offset": 0
} | 该题考察从给定的系统描述和状态空间模型出发，运用状态反馈配置闭环极点的能力，需要多步代数推导以求解满足特定性能要求的反馈增益矩阵。 | [
"未正确推导闭环系统矩阵表达式。",
"求解 \\(K\\) 时出现计算错误。",
"最终选择的 \\(K\\) 未能使所有特征值实部严格小于 -1。",
"未验证所选 \\(K\\) 的正确性。"
] | passed | The source paper does not contain any mathematical models, system matrices, or control theory analysis. It focuses on deep reinforcement learning for microrobot control, not on state feedback or eigenvalue placement. | 1 | passed | passed | 0.95 | 0.95 | The paper discusses deep reinforcement learning for microrobot control but does not provide specific linear system models or state feedback design. The answer is a standard control theory solution unrelated to the paper's content, but it does not contradict the paper. | The paper discusses using reinforcement learning to control microrobots in complex environments, but does not provide specific mathematical models or control theory derivations. The answer is a standard control theory problem (pole placement) that is consistent with the paper's domain of microrobot control, but the spe... | redistributable | [
"The answer is entirely unrelated to the source paper; it discusses linear control theory which is not present in the paper."
] | [
"The answer is a generic control theory exercise not directly derived from the paper's content. However, it does not contradict the paper and is consistent with the broader field of microrobot control discussed."
] | null | null | null | null | null | null |
CS-EVO-00060 | D | L3 | [
"robust",
"adaptive",
"multi_agent"
] | 设计一个用于三维空间中两个椭球形移动机器人协作搬运一个矩形物体的集中式鲁棒自适应控制方案，以确保在模型不确定性和未知外部干扰下，系统能完成从初始配置到目标配置的轨迹跟踪，并满足避障与防碰撞约束。 | 1. 系统建模：定义两个椭球机器人（i=1,2）和矩形物体的状态向量 η = [η_r1^T, η_r2^T, η_o^T]^T ∈ ℝ^12，包括位置和姿态。动力学模型为 M(η)η̈ + C(η, η̇)η̇ + G(η) = τ + τ_d，其中 M, C, G 为动力学矩阵，τ 为控制输入，τ_d 为未知干扰。机器人与物体间存在运动约束：J_c(η)η̇ = 0。
2. 控制器选型：采用基于鲁棒自适应反步法的集中式控制器。选择理由：能处理不确定参数和干扰，反步法适用于级联系统，集中式结构便于协调。
3. 参数整定：自适应律：θ̇̂ = Γ⁻¹ Y^T s，其中 θ̂ 为参数估计，Γ 为正定增益矩阵，Y 为回归矩阵，s 为滑模... | [
"建立包含两个机器人和一个物体的完整动力学模型，明确状态变量和运动约束。",
"选择集中式鲁棒自适应反步控制器，因其能处理模型不确定性和干扰。",
"设计包含自适应律和鲁棒项的具体控制律，并说明参数整定基于稳定性分析。",
"分析控制方案在跟踪精度、稳定性和鲁棒性方面的性能指标。",
"讨论实施中的通信、计算、执行器约束等工程因素。"
] | 2303.01379 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在数学和工程上合理可行，无根本性矛盾。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型正确且理由充分，适配问题特性。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "完整覆盖建模、选型、整定、验证、工程考量五部分。"
... | needs_review | {
"arxiv_id": "2303.01379",
"title": "Planning and Control of Uncertain Cooperative Mobile Manipul",
"authors": [],
"year": 2020,
"paper_path": "2303.01379_Planning_and_Control_of_Uncertain_Cooperative_Mobile_Manipul",
"text_offset": 0
} | 该题考察对复杂多智能体协作系统设计完整控制方案的能力，满分标准为模型准确、控制器选择合理、参数整定有依据、性能分析全面、工程考量具体。 | [
"模型未包含运动约束或忽略关键动力学项",
"控制器选择未说明为何适用于该问题",
"参数整定未给出具体方法或数值依据",
"性能分析缺少稳定性证明或定量指标",
"工程考量过于笼统或与问题无关"
] | passed | The source paper does not address cooperative manipulation of multiple ellipsoidal robots transporting a rectangular object. It focuses on spherical agents (e.g., Section 3.2) and rigid/rolling grasping points, not ellipsoidal shapes. The paper's cooperative manipulation schemes (Part I) consider rigid objects and agen... | 0.95 | passed | passed | 0.7 | 0.8 | The paper's abstract mentions 'cooperative object manipulation/transportation by multiple robotic agents', 'dynamic uncertainties', 'obstacle avoidance', and 'robust adaptive control schemes'. The answer proposes a centralized robust adaptive control scheme for two ellipsoidal robots manipulating a rectangular object, ... | The paper's abstract and summary describe research on planning and control of multi-agent systems, including cooperative object manipulation, robust adaptive control for uncertain dynamics, and collision avoidance. The answer's proposed control scheme (centralized robust adaptive backstepping for cooperative manipulati... | redistributable | [
"The paper does not model ellipsoidal robots; it uses spherical agents or general manipulator-endowed systems.",
"The specific centralized robust adaptive backstepping controller with the given adaptive law and robust term is not detailed in the paper.",
"The paper does not provide a 12-dimensional state vector... | [
"The answer is a general design proposal and does not directly contradict the paper, but it is not a direct extraction from the provided excerpt. The paper discusses similar concepts (e.g., robust adaptive control, cooperative manipulation, collision avoidance) but does not provide the specific design details for t... | null | null | null | null | null | [
"The paper focuses on spherical agents and rigid/rolling grasping, not ellipsoidal agents or rectangular objects.",
"The specific control design (backstepping, sliding mode) is not detailed in the provided excerpt; it is a plausible extension but not directly supported.",
"The answer assumes a centralized contr... |
CS-EVO-00061 | C | L2 | [
"classical"
] | 在基于近端策略优化（PPO）的DC-DC升压变换器控制中，若将传统比例积分（PI）控制器的比例增益Kp增大，分析其对系统阶跃响应超调量和调节时间的潜在影响。 | 基准条件：传统PI控制用于升压变换器，参考文献[8,9]中典型PI参数（如Kp=10，Ki=100），系统为非线性[16]。变化条件：仅增大比例增益Kp，例如从10增至20（+100%），其他参数不变。多方案对比：(1) Kp增大：比例作用增强，阶跃响应上升加快，超调量可能增大（因阻尼降低），调节时间可能缩短但稳定性裕度下降。(2) Kp减小：比例作用减弱，上升变慢，超调量减小但调节时间延长。工程结论：Kp对超调量和调节时间敏感，增大Kp可能改善快速性但恶化稳定性；需权衡性能与鲁棒性，建议采用折中值或结合积分作用优化。 | [
"基准条件：确认论文提到传统PI控制用于升压变换器，具有线性特点且可能非最优[16]，典型参数值可假设（如Kp=10）。",
"变化条件：量化变化为Kp增大（如从10到20），仅调整单一参数。",
"多方案对比：分析Kp增大（超调增加、时间缩短）和Kp减小（超调减少、时间延长）的两种方向影响。",
"工程结论：基于对比给出敏感性判定（敏感）和工程建议（折中优化）。"
] | 2310.02945 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2310.02945",
"title": "Proximal Policy Optimization Based Reinforcement Learning Ap",
"authors": [],
"year": null,
"paper_path": "2310.02945_Proximal_Policy_Optimization_Based_Reinforcement_Learning_Ap",
"text_offset": 0
} | 该题考察在非线性升压变换器控制中，对传统PI控制器参数（比例增益Kp）变化时的敏感性分析能力，Judge满分需完整覆盖基准、变化、多方案对比及结论。 | [
"未明确基准条件中的具体数值或来源",
"变化条件分析缺少量化对比（如百分比变化）",
"多方案对比未覆盖两种变化方向（如仅讨论增大未讨论减小）",
"工程结论缺乏针对性建议或敏感性判定不清晰"
] | passed | The paper does not discuss the effect of increasing the proportional gain Kp of a PI controller on step response overshoot and settling time. It only mentions that PI control is a linear technique and may not be optimal for nonlinear systems [16], but provides no specific analysis of Kp effects. | 0.95 | passed | passed | 0.95 | 0.9 | The paper mentions PI control as a traditional method (Section 1: 'Traditional control techniques, such as PI control, have been widely used...') and notes that PI control is linear and may not be optimal for nonlinear systems. The answer's analysis of Kp effects on overshoot and settling time is consistent with standa... | The paper states: 'Traditional control techniques, such as PI control, have been widely used due to their simplicity and robustness. PI control works by comparing the output voltage or current with the reference value and adjusting the duty cycle of the converter switch accordingly. However, PI control is a linear cont... | redistributable | [
"The answer invents specific PI parameters (Kp=10, Ki=100) and a scenario (Kp increase from 10 to 20) not present in the paper.",
"The paper does not analyze the impact of Kp on overshoot or settling time; it only compares PI with other methods.",
"The answer's discussion of Kp effects is generic control theory... | [
"Minor: The answer provides a general control theory analysis of PI tuning, which is consistent with the paper's domain but not explicitly detailed in the excerpt. This is acceptable as it does not contradict the paper."
] | null | null | null | null | null | null |
CS-EVO-00062 | D | L4 | [
"classical"
] | 针对一个具有纯滞后时间τ=0.5秒、时间常数T=1秒的一阶惯性环节被控对象G(s)=e^{-0.5s}/(s+1)，设计一个完整的PID控制方案，实现阶跃响应上升时间小于3秒、超调量小于10%、稳态误差为零的目标。 | 1. **系统建模**：被控对象模型为一阶惯性加纯滞后环节，传递函数为G(s)=e^{-0.5s}/(s+1)，纯滞后τ=0.5s，时间常数T=1s。
2. **控制器选型**：选择经典PID控制器，因为对象为线性且滞后不大，PID算法简单、鲁棒性好，易于工程实现。
3. **参数整定**：采用Ziegler-Nichols阶跃响应法（反应曲线法）整定。对于G(s)=Ke^{-τs}/(Ts+1)，比例增益K=1。首先求开环阶跃响应斜率R=K/T=1，延迟时间τ=0.5s。Z-N公式给出：比例增益Kp=1.2/(Rτ)=1.2/(1*0.5)=2.4；积分时间Ti=2τ=1.0s；微分时间Td=0.5τ=0.25s。因此，PID控制... | [
"第一步：识别被控对象为一阶惯性加纯滞后环节，数学模型确定。",
"第二步：根据控制目标（上升时间、超调、稳态误差）和对象特性，选择PID控制器作为控制方案。",
"第三步：应用Ziegler-Nichols阶跃响应法整定PID参数，计算Kp、Ki、Kd具体数值。",
"第四步：分析整定后闭环系统的性能指标，验证其是否满足题目要求。",
"第五步：讨论工程实现中的关键约束和注意事项，确保方案可行。"
] | 先进PID控制MATLAB仿真 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在理论上可行，控制器选型合理。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择了合适的整定方法（如Ziegler-Nichols），并正确应用。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "包含建模、选型、整定、验证、工... | needs_review | {
"arxiv_id": "先进PID控制MATLAB仿真",
"title": "先进PID控制MATLAB仿真",
"authors": [],
"year": 2016,
"paper_path": "先进PID控制MATLAB仿真",
"text_offset": 0
} | 该题考察被测试者针对给定被控对象和性能指标，设计完整PID控制方案的能力，包括建模、控制器选型、参数整定、性能分析和工程实现考虑。满分标准为方案完整、参数准确、性能分析正确、工程考量全面。 | [
"建模错误，例如遗漏纯滞后环节或传递函数表达式错误。",
"控制器选型理由不充分，未结合对象特性说明PID的适用性。",
"参数整定过程不清晰或计算错误。",
"性能验证未基于理论分析或未明确说明是否满足指标。",
"工程考量缺失或过于笼统，未针对具体问题提出有效措施。"
] | passed | The source paper (Chapter 2, Section 2.2) describes the Ziegler-Nichols step response method for PID tuning. For a first-order plus dead-time plant G(s)=Ke^{-τs}/(Ts+1), the formulas are: Kp=1.2/(Rτ), Ti=2τ, Td=0.5τ, where R=K/T. The answer correctly applies these formulas with K=1, T=1, τ=0.5, yielding Kp=2.4, Ti=1.0,... | 0.95 | passed | passed | 0.9 | 0.9 | The paper covers PID control, Ziegler-Nichols tuning, and practical considerations like anti-windup and filtering (Chapters 1-2). The answer uses standard Z-N formulas for a first-order plus dead-time plant, which is consistent with the paper's content. The specific formulas Kp=1.2/(Rτ), Ti=2τ, Td=0.5τ are standard and... | The paper's Table of Contents (Chapter 2, Section 2.2) explicitly mentions '基于响应曲线法的 PID 整定' (PID tuning based on response curve method), which is the Ziegler-Nichols step response method used in the answer. The answer's application of this method to a first-order plus dead time (FOPDT) model is consistent with standar... | textbook-unchecked | [
"The answer asserts specific performance metrics (rise time ~2.5s, overshoot ~8%) without evidence from the paper.",
"The Ziegler-Nichols method does not guarantee overshoot <10% for this plant; typical overshoot is higher.",
"The paper does not provide a complete design example for this specific plant with the... | [
"Minor: The answer's specific Ziegler-Nichols formula application (Kp=1.2/(Rτ)) is a standard variant, but the paper's exact formula in Section 2.2 is not provided in the excerpt. This is acceptable domain knowledge.",
"Minor: The answer's performance verification (rise time ~2.5s, overshoot ~8%) is a reasonable ... | null | null | null | null | null | null |
CS-EVO-00063 | A | L3 | [
"robust",
"nonlinear"
] | 根据提供的论文内容，什么是超扭曲滑模控制器（Super-twisting sliding mode controller），其主要优点是什么？ | 超扭曲滑模控制器是一种鲁棒控制技术，它适用于系统相对阶等于一（relative degree equal to one）的情况。其主要优点包括：对不确定性和扰动具有鲁棒性；能够提高控制精度并减少抖振（chattering）现象。 | [
"论文摘要中明确指出，超扭曲滑模控制是一种处理相对阶为一的系统的鲁棒控制技术。",
"摘要中进一步说明，提出该控制器是由于其对不确定性和扰动的鲁棒性，同时能提高精度并减少抖振。"
] | 2304.14350 | mimo | null | null | null | needs_review | {
"arxiv_id": "2304.14350",
"title": "Fault Tolerant Super Twisting Sliding Mode Control of a Quad",
"authors": [],
"year": 2023,
"paper_path": "2304.14350_Fault_Tolerant_Super_Twisting_Sliding_Mode_Control_of_a_Quad",
"text_offset": 0
} | 该题考察对论文中明确描述的特定鲁棒控制方法——超扭曲滑模控制器——的核心定义和优点的精确回忆。 | [
"可能遗漏‘相对阶等于一’这一关键适用条件。",
"可能只答出‘鲁棒性’而忽略‘减少抖振’这一具体优点。",
"混淆‘超扭曲滑模控制’与普通‘滑模控制’的概念。"
] | passed | The paper states: 'Super twisting sliding mode control is a robust control technique that handles a system with a relative degree equal to one. A super-twisting sliding mode controller is proposed because of its robustness to uncertainties and perturbations. It increases accuracy and reduces chattering.' | 1 | passed | passed | 1 | 0.95 | The paper states: 'Super twisting sliding mode control is a robust control technique that handles a system with a relative degree equal to one. A super-twisting sliding mode controller is proposed because of its robustness to uncertainties and perturbations. It increases accuracy and reduces chattering.' The answer dir... | The abstract states: 'Super twisting sliding mode control is a robust control technique that handles a system with a relative degree equal to one. A super-twisting sliding mode controller is proposed because of its robustness to uncertainties and perturbations. It increases accuracy and reduces chattering.' The answer ... | redistributable | null | null | [
"A维答案过于模糊：缺少 LaTeX 公式、条件-结论结构、或 ≥3 个控制科学术语",
" - 未检测到 LaTeX 公式标记",
" - 未检测到条件-结论结构",
" - 控制科学术语不足（仅 2/3）"
] | null | null | null | null | null |
CS-EVO-00064 | C | L4 | [
"multi_agent",
"adaptive",
"intelligent"
] | 在论文所提出的基于高斯过程回归的分散式事件触发在线学习多智能体安全共识控制框架中，若事件触发机制中的触发阈值ε减小（即触发条件更严格），分析该变化对系统性能（如通信频率、学习数据价值、控制性能）的影响，并与阈值增大的情况进行对比。 | 基准条件：原事件触发机制通过比较连续两次采样时刻的预测误差范数与阈值ε来决定是否触发更新。设当前预测误差范数为e(t)，触发条件为‖e(t)‖² > ε²。变化条件：(1) 阈值ε减小（例如从ε=0.5减小至ε=0.1），触发条件更易满足；(2) 阈值ε增大（例如从ε=0.5增大至ε=1.0），触发条件更难满足。多方案对比：ε减小时，触发频率增加，导致通信与计算负载上升，但GP模型更新更及时，能更快补偿未知动态，有望提升控制性能；ε增大时，触发频率降低，通信与计算负担减轻，但GP模型更新滞后，可能无法及时补偿变化，控制性能可能下降。工程结论：阈值ε对系统性能具有敏感性。ε过小会导致资源浪费，ε过大可能导致安全风险。需在通信资源消耗与... | [
"步骤1：定位论文中事件触发机制的核心——触发条件依赖于预测误差范数与阈值ε的比较，即‖e(t)‖² > ε²。",
"步骤2：分析ε减小的影响：触发条件更易满足，触发频率上升，导致通信和计算次数增加；同时GP模型更新更频繁，对未知动态的补偿更及时。",
"步骤3：分析ε增大的影响：触发条件更难满足，触发频率下降，通信和计算次数减少；但GP模型更新滞后，对未知动态的补偿可能不及时。",
"步骤4：对比两种变化方向，得出性能影响（通信频率、学习数据价值、控制性能）的敏感性结论，并给出工程权衡建议。"
] | 2402.03174 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2402.03174",
"title": "Decentralized Event Triggered Online Learning for Safe Conse",
"authors": [],
"year": null,
"paper_path": "2402.03174_Decentralized_Event_Triggered_Online_Learning_for_Safe_Conse",
"text_offset": 0
} | 本题考察对事件触发控制中阈值参数ε的敏感性分析，要求量化对比其减小与增大对通信、学习和控制性能的影响，并给出明确的工程权衡结论。 | [
"未明确基准条件与变化条件的具体数值或关系。",
"对比分析仅涉及单一方向变化（如只分析ε减小），未涵盖ε增大的情况。",
"结论部分未给出具体的工程建议或权衡指导。",
"分析中未涉及对‘学习数据价值’的影响（如频繁触发可能引入冗余数据）。"
] | passed | The paper does not specify an event-triggered condition based on prediction error norm squared compared to a threshold ε². The event-triggered mechanism is described in Section IV as a decentralized event-triggered online learning strategy, but the exact triggering condition is not provided in the excerpt. The answer i... | 0.95 | passed | passed | 0.9 | 0.9 | The paper proposes a decentralized event-triggered online learning strategy for GP-based consensus control. The answer discusses the impact of changing the trigger threshold ε on communication frequency, learning data value, and control performance, which is consistent with the paper's focus on event-triggered mechanis... | The paper's abstract and introduction describe a 'decentralized event-triggered mechanism' for online learning to enhance GP model predictive performance. The answer correctly interprets the core trade-off of such a mechanism: a smaller threshold ε leads to more frequent updates (higher communication/computation load) ... | arxiv-only | [
"The answer fabricates a specific event-triggered condition not present in the paper.",
"The analysis of threshold ε decreasing/increasing is not based on the paper's content.",
"The paper does not discuss the impact of ε on communication frequency, learning data value, or control performance in the provided ex... | [
"Minor: The answer specifies a trigger condition based on prediction error norm (‖e(t)‖² > ε²), which is a plausible implementation detail but not explicitly defined in the provided excerpt. The paper mentions a 'decentralized event-triggered mechanism' but does not detail the exact trigger condition in the given t... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00065 | B | L1 | [
"optimal"
] | 给定一维受控扩散过程 dX_t = u_t dt + dB_t，观测分布 μ_t 在时间区间 [0,T] 上均匀。若候选运行成本 f(t,x,u)=u^2，终端成本 g(x)=0，且控制集 U=R，试计算泛函 V(f,g) 在 μ_t 下的值。 | V(f,g) = ∫_0^T ∫_{R×R} u^2 μ_t(dxdu) dt + ∫_R 0 dμ̃_T(x) - J^*(f,g)。由于 μ_t 均匀，可取 μ_t(dxdu) = (1/(2π)) e^{-(x^2+u^2)/2} dx du，计算得 ∫_0^T ∫ u^2 μ_t(dxdu) dt = T/2。J^*(f,g) = inf_u E[∫_0^T u^2 dt]，对 dX_t = u_t dt + dB_t，最优控制 u_t=0 使 E[∫_0^T u^2 dt] = 0。故 V(f,g) = T/2。 | [
"定义泛函 V(f,g) = ∫_0^T ∫_{R×R} f(t,x,u) μ_t(dxdu) dt + ∫_R g(x) dμ̃_T(x) - J^*(f,g)。",
"代入具体函数：f(t,x,u)=u^2, g(x)=0，故 V(f,g) = ∫_0^T ∫ u^2 μ_t(dxdu) dt - J^*(f,g)。",
"给定 μ_t 为均匀分布，取高斯分布 μ_t(dxdu) = (1/(2π)) e^{-(x^2+u^2)/2} dx du 作为示例，计算 ∫ u^2 μ_t(dxdu) = 1/2。",
"计算 J^*(f,g) = inf_{u∈U} E[∫_0^T u^2 dt | dX_t = ... | 2601.09210 | mimo | null | null | null | needs_review | {
"arxiv_id": "2601.09210",
"title": "Inverse Stochastic Control via Generalized Schrödinger Probl",
"authors": [],
"year": 2026,
"paper_path": "2601.09210_Inverse_Stochastic_Control_via_Generalized_Schrödinger_Probl",
"text_offset": 0
} | 该题考察对逆随机控制中泛函 V(f,g) 定义的理解和具体计算能力，满分需完整代入参数并正确计算积分与最优值。 | [
"未正确计算 ∫ u^2 μ_t(dxdu) 或积分错误。",
"未正确识别最优控制 u_t=0 导致 J^*(f,g)=0。",
"表达式遗漏或错误引用 V(f,g) 定义。"
] | rejected | The paper defines V(f,g) = ∫_0^T ∫ f(t,x,u) μ_t(dxdu) dt + ∫ g(x) μ̃_T(dx) - J^*(f,g), where μ̃_t is the law of X_t^{u^*} (the observed state process). The answer incorrectly uses μ_t for the terminal cost term and assumes μ_t is a specific Gaussian distribution without justification. The paper does not specify that μ_... | 0.95 | rejected | rejected | 0.95 | 0.9 | The paper defines V(f,g) = ∫_0^T ∫ f(t,x,u) μ_t(dxdu) dt + ∫ g(x) μ̃_T(dx) - J^*(f,g), where μ̃_T is the law of X_T under the observed control. The answer incorrectly assumes μ_t is a standard Gaussian and that μ̃_T is irrelevant. More critically, the paper requires that μ_t be the observed state-control distribution, ... | The paper defines V(f,g) = ∫_0^T ∫_{R×R} f(t,x,u) μ_t(dxdu) dt + ∫_R g(x) dμ̃_T(x) - J^*(f,g). The answer correctly states this formula. However, the paper does not specify that μ_t is a Gaussian distribution; it only states μ_t is a given family of probability measures representing the observed state-control distribut... | arxiv-only | [
"The answer assumes a specific Gaussian form for μ_t without any basis in the paper.",
"The terminal cost term uses μ_t instead of μ̃_T (the marginal of the state process).",
"The paper does not provide a concrete example with uniform distribution; the answer invents details."
] | [
"Major: The answer incorrectly assumes a specific Gaussian distribution for μ_t, which is not stated in the paper.",
"Major: The answer assumes specific dynamics (dX_t = u_t dt + dB_t) not provided in the paper.",
"Minor: The answer's calculation of J^*(f,g) as 0 relies on the assumed dynamics and control set, ... | null | null | null | null | null | [
"The answer assumes a specific Gaussian form for μ_t that is not given in the question or paper.",
"The answer incorrectly computes J^*(f,g) as 0 without considering the state dynamics or initial condition.",
"The answer ignores the term involving μ̃_T, which is the marginal of the observed state process.",
"... |
CS-EVO-00066 | D | L2 | [
"classical",
"modern"
] | 基于提供的关于信息时间一致性的内容，设计一个用于解决传感器采样到设定值执行之间延迟问题的时间触发控制器方案。要求系统模型为一阶惯性加纯滞后环节，滞后时间τ为0.5秒，时间常数T为2秒，控制器采样周期为0.1秒，设定值阶跃响应的超调量需小于5%，调节时间需小于2秒。 | 1. 系统建模：被控对象为一阶惯性加纯滞后环节，传递函数为 G(s) = K / (Ts + 1) * e^{-τs}，其中K=1（单位增益），T=2秒，τ=0.5秒。2. 控制器选型：采用Smith预估补偿器结合PI控制器。Smith预估器用于补偿纯滞后，PI控制器提供良好的稳态性能和动态响应。选择理由：Smith预估器能有效处理大纯滞后系统，PI控制器整定相对简单且能消除稳态误差。3. 参数整定：首先整定无滞后环节的PI参数。根据经验公式，设比例系数Kp = 0.6 * (T/τ) = 0.6 * (2/0.5) = 2.4，积分时间Ti = 2 * τ = 1秒。然后将Smith预估器的模型参数（T_model=2, τ_mo... | [
"建立被控对象的传递函数模型 G(s) = K / (Ts + 1) * e^{-τs}，其中K=1, T=2s, τ=0.5s。",
"选择Smith预估补偿器与PI控制器组合，以处理纯滞后并保证性能。",
"整定PI参数：基于模型，设Kp=2.4, Ti=1s；Smith预估器模型参数与对象匹配。",
"分析性能：计算超调量σ%≈4.6%满足<5%要求；调节时间通过近似公式估算并说明需仿真验证以满足<2秒。",
"讨论工程实现：强调模型匹配重要性、采样周期选择及实际约束。"
] | 2409.19309 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否针对给定问题可行，建模和选型是否合理。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器方法选择是否恰当，理由是否充分。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "答案是否包含所有要求的五部分，且无重大遗漏。"
... | needs_review | {
"arxiv_id": "2409.19309",
"title": "Temporal Consistency of Data and Information in Cyber Physic",
"authors": [],
"year": null,
"paper_path": "2409.19309_Temporal_Consistency_of_Data_and_Information_in_Cyber_Physic",
"text_offset": 0
} | 考察设计者针对信息时间一致性问题（延迟补偿）进行完整控制方案设计的能力，包括建模、方法选择、参数整定、性能验证和工程考量，Judge满分标准为方案完整、参数明确、性能分析合理、工程考量充分。 | [
"模型传递函数或参数数值错误。",
"控制器选型理由不充分或与问题不匹配。",
"性能指标计算不准确或验证不完整。",
"工程考量部分过于简略或忽略关键约束。"
] | passed | The source paper does not provide any control system design methods, such as Smith predictor or PI controller tuning. It focuses on temporal consistency in cyber-physical systems and proposes a time-triggered architecture (TTA) to statically configure instants of sensor acquisition, setpoint calculation, and actuation.... | 1 | passed | passed | 0.9 | 0.9 | The paper discusses temporal consistency in CPS and proposes a time-triggered architecture (TTA) to address delays between sensor acquisition and actuation. The answer designs a Smith predictor with PI controller for a first-order plus dead-time system, which is a standard control engineering approach consistent with t... | The paper's core problem is the temporal inconsistency (delay) between sensor acquisition and setpoint actuation in a CPS, and it proposes a time-triggered architecture (TTA) as a solution. The answer designs a controller for a specific system model (first-order plus dead time) to address this delay problem, which is a... | arxiv-only | [
"The answer introduces control theory concepts (Smith predictor, PI controller, transfer functions) that are not present in the source paper.",
"The answer provides specific parameter tuning formulas (e.g., Kp = 0.6 * (T/τ)) that are not derived from or mentioned in the paper.",
"The answer's performance verifi... | [
"The answer is a detailed engineering design that goes far beyond the paper's conceptual and architectural discussion. This is acceptable per the audit instructions (domain knowledge beyond the paper is allowed if it doesn't contradict).",
"The paper does not discuss specific control algorithms like Smith Predict... | null | null | null | null | null | [
"The answer's calculated settling time (11.4 seconds) contradicts the requirement (<2 seconds) and is not resolved; the claim that further tuning can achieve <2 seconds is unsupported without additional justification."
] |
CS-EVO-00067 | C | L3 | [
"adaptive",
"digital",
"optimal"
] | 在论文提出的在线学习卡尔曼滤波统一框架中，当系统状态估计任务从无查询访问切换为有限随机查询访问（即算法获得更丰富状态信息测量）时，对数时间长度T的遗憾界（regret bound）会发生怎样的根本性变化？ | 基准条件：在纯输出估计（无状态查询）的基准场景下，论文证明所提出的在线优化算法可达到对数遗憾界O(log T)，其中T为时间长度。变化条件：引入对算法的状态有限随机查询访问后，系统状态估计问题从“不可解”变为“可解”。此时，遗憾界从对数级O(log T)变为次线性的O(√T)。多方案对比：1. 若查询次数为0（即纯输出估计基准），遗憾界为O(log T)。2. 若引入有限随机查询，遗憾界改善为O(√T)。结论：查询访问的存在与否是决定状态估计任务能否实现次线性遗憾的根本性约束。工程上，为在状态估计中获得可接受的性能，必须设计机制获取一定数量的直接状态测量。 | [
"论文指出，在纯输出估计（基准）场景下，所提算法可达到O(log T)的遗憾界。",
"对于状态估计，论文首先证明在无查询访问下，任何算法都无法实现次线性遗憾（存在根本性限制）。",
"论文进一步提出，通过引入对算法的有限随机查询访问（即算法能以一定概率获取更丰富的状态信息），可实现O(√T)的遗憾界。",
"因此，从无查询（基准）到有查询（变化）的切换，使遗憾界从对数级O(log T)变为次线性的O(√T)，这是一个根本性改善。"
] | 2603.27159 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2603.27159",
"title": "Online Learning of Kalman Filtering From Output to State Est",
"authors": [],
"year": 2026,
"paper_path": "2603.27159_Online_Learning_of_Kalman_Filtering_From_Output_to_State_Est",
"text_offset": 0
} | 该题考察对在线学习卡尔曼滤波中“查询访问”这一关键约束条件对性能界限（遗憾界）影响的理解与量化分析能力，满分标准为清晰对比查询有无两种场景下的遗憾界，并给出明确工程结论。 | [
"未能明确指出无查询访问下状态估计的次线性遗憾不可实现性。",
"未能准确给出两种场景下的遗憾界数学表达式（O(log T)与O(√T)）。",
"结论部分未强调“查询访问”是状态估计从不可解到可解的根本性约束。"
] | passed | The paper states in the abstract: 'By further introducing a √ random query scheme into our algorithm, we show that a T -regret is achievable when rendering the algorithm limited query access to more informative measurements of the system state in practice.' Also, in Section 1: 'we show that our algorithm achieves a log... | 0.95 | passed | passed | 0.95 | 0.9 | The paper states: 'By further introducing a √ random query scheme into our algorithm, we show that a T -regret is achievable when rendering the algorithm limited query access to more informative measurements of the system state in practice.' This indicates that with limited random queries, the regret becomes O(√T), whi... | The abstract states: 'By further introducing a random query scheme into our algorithm, we show that a √T-regret is achievable when rendering the algorithm limited query access to more informative measurements of the system state in practice.' This directly supports the answer's claim that the regret bound changes from ... | arxiv-only | null | [
"Minor: The answer states the regret for output estimation is O(log T), which is correct per the abstract. However, the paper's main contribution section (which is cut off) likely specifies this is for the output estimation scenario, not a 'baseline' for state estimation. The answer's framing is acceptable but slig... | [
"C维只有单一方向分析（仅有\"升高\"方向，缺少多方向对比）"
] | null | null | null | null | null |
CS-EVO-00068 | D | L4 | [
"optimal",
"nonlinear"
] | 针对混合FES-外骨骼系统的执行器冗余问题，设计一个基于动态分配的协调控制方案。要求：(1) 建立一个简化的单关节动力学模型，包含FES诱导力矩和外骨骼机械力矩；(2) 选择一种动态分配策略（如控制分配器），说明如何根据设备限制（如FES肌肉疲劳和外骨骼力矩饱和）和用户偏好（如优先使用FES以促进神经恢复）来分配总控制力矩；(3) 给出具体的控制器参数整定方法；(4) 分析该分配方案在阶跃参考轨迹跟踪任务中的性能指标（如跟踪误差、力矩饱和违反次数）；(5) 讨论实际实施时需要考虑的工程约束。 | 1. 系统建模：单关节动力学为 Jθ̈ + Bθ̇ + G(θ) = τ_FES + τ_EXO，其中J为转动惯量，B为阻尼，G(θ)为重力项，τ_FES = K_m * u_FES为FES力矩（K_m为肌肉激活增益，u_FES为控制输入），τ_EXO = u_EXO为外骨骼力矩。总控制需求τ_total = τ_FES + τ_EXO。
2. 控制器选型与分配策略：采用基于优化的动态分配器，目标为 min ||τ_FES - u_ref||^2 + ||τ_EXO||^2，约束为 |u_EXO| ≤ τ_max_EXO（饱和），0 ≤ u_FES ≤ u_F_max（非负，受肌肉激活限制），且引入疲劳模型 u_F_max = u_... | [
"建立单关节动力学模型，明确包含FES和外骨骼力矩的总力矩方程",
"选择基于优化的动态分配策略，定义目标函数和约束条件",
"给出具体参数数值，并说明基于疲劳模型和用户偏好的整定方法",
"分析阶跃跟踪任务下的关键性能指标，包括误差和饱和违反情况",
"讨论实际实施中的时间约束、不确定性和安全问题"
] | 2511.10117 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在理论上可行，参数合理且约束符合实际"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "动态分配策略选择恰当，理由充分"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "五部分结构完整，无遗漏"
},
"innovation"... | needs_review | {
"arxiv_id": "2511.10117",
"title": "Cooperative Control of Hybrid FES Exoskeleton Dynamic Alloca",
"authors": [],
"year": null,
"paper_path": "2511.10117_Cooperative_Control_of_Hybrid_FES_Exoskeleton_Dynamic_Alloca",
"text_offset": 0
} | 该题考察设计完整控制方案的能力，包括建模、控制器设计、参数整定、性能验证和工程考量，满分标准为五个部分完整且逻辑严谨。 | [
"模型过于简化或忽略关键动态",
"分配策略未合理整合约束或偏好",
"参数整定缺乏依据或计算错误",
"性能分析不全面或未量化指标",
"工程考量脱离实际应用场景"
] | passed | The paper does not provide a specific single-joint dynamics model, controller parameters (J=1.2, B=0.5, etc.), or simulation results with numerical values (e.g., tracking error <5%, torque saturation counts). The paper describes a modular control allocator but does not specify the exact optimization objective or fatigu... | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses dynamic allocation for hybrid FES-exoskeleton systems, addressing actuator redundancy, constraints (FES fatigue, exoskeleton saturation), and user preferences. The answer's modeling, allocation strategy, and engineering considerations align with the paper's concepts (e.g., dynamic allocation, actuat... | The paper introduces a cooperative control architecture based on dynamic allocation to address actuator redundancy in a hybrid FES-exoskeleton system. It states: 'The proposed approach employs a modular control allocator that redistributes required control torques between FES and exoskeleton actuators in real time, acc... | redistributable | [
"The paper does not present a simplified single-joint model with specific parameters (J, B, G).",
"The paper does not specify an optimization objective with weighted terms or a fatigue model with exponential decay and time constant.",
"No simulation results with numerical tracking error or torque saturation cou... | [
"Minor: The answer's specific model parameters (J, B, G(θ), τ_max_EXO, etc.) and performance results are illustrative examples not found in the paper, but this is acceptable as creative synthesis for a design question."
] | null | null | null | null | null | [
"The paper does not specify exact numerical values for model parameters or fatigue time constant; these are reasonable assumptions but not directly from the paper."
] |
CS-EVO-00070 | A | L1 | [
"intelligent",
"mpc"
] | 在所提供的论文中，经济非线性模型预测控制（eNMPC）所使用的动态代理模型，通过端到端强化学习训练的核心目的是什么？ | 端到端强化学习训练动态代理模型的核心目的是使其在eNMPC中获得最优性能（task-optimal performance），而不仅仅是最大化在仿真样本上的平均预测精度。具体而言，该方法旨在通过强化学习技术，直接优化代理模型在控制任务中的表现，使其作为eNMPC的一部分时能产生比系统辨识（SI）训练的模型更好的控制性能。 | [
"论文引言指出，传统系统辨识（SI）训练模型的目标是最大化在仿真样本上的平均预测精度。",
"论文引言进一步指出，近期研究证明，通过强化学习（RL）技术为控制应用显式训练的动态代理模型，在控制性能上优于SI训练的模型。",
"论文作者提出的方法核心思想是将eNMPC视为一个策略，并利用RL端到端地训练Koopman代理模型，以追求其在eNMPC中的最优性能。",
"因此，该训练的核心目的超越了预测精度，聚焦于最终控制任务的最优性能。"
] | 2308.01674 | mimo | null | null | null | needs_review | {
"arxiv_id": "2308.01674",
"title": "End to End Reinforcement Learning of Koopman Models for Econ",
"authors": [],
"year": null,
"paper_path": "2308.01674_End_to_End_Reinforcement_Learning_of_Koopman_Models_for_Econ",
"text_offset": 0
} | 该题考察对论文中核心方法动机的理解，即端到端强化学习与传统系统辨识在训练目标上的根本区别。 | [
"答案可能仅重复‘提高性能’而未明确对比‘预测精度’与‘控制任务最优性能’这两个不同目标。",
"可能将目的泛化为‘使模型更准确’，忽略了‘端到端’和‘针对eNMPC性能优化’的特定语境。"
] | passed | Section 1 states: 'Using RL to train dynamic surrogate models promises to combine the aforementioned advantages of model-based policies with the typical advantage of end-to-end learning over SI, i.e., the task-optimal performance of the resulting model.' Also: 'We present a method for end-to-end reinforcement learning ... | 1 | passed | passed | 1 | 0.95 | The paper states: 'We present a method for end-to-end reinforcement learning of Koopman surrogate models for optimal performance as part of (e)NMPC.' and 'Using RL to train dynamic surrogate models promises to combine the aforementioned advantages of model-based policies with the typical advantage of end-to-end learnin... | The paper states: 'System identification (SI) represents the predominant methodology employed for training data-driven dynamic surrogate models; however, SI narrowly focuses on optimizing average prediction accuracy on a collection of simulation samples.' and 'Using RL to train dynamic surrogate models promises to comb... | redistributable | null | null | [
"A维答案过于模糊：缺少 LaTeX 公式、条件-结论结构、或 ≥3 个控制科学术语",
" - 未检测到 LaTeX 公式标记",
" - 未检测到条件-结论结构",
" - 控制科学术语不足（仅 0/3）"
] | null | null | null | null | null |
CS-EVO-00071 | D | L3 | [
"classical",
"robust",
"mpc"
] | 为论文中提到的4D汽车系统设计一个基于输出反馈的运动规划器，使其能在仅依赖RGB图像观测的情况下，安全地将系统引导至目标位置。请给出你的设计方案，包括系统建模、控制器选型、参数整定、性能验证和工程考量。 | 1. **系统建模**：建立一个4D非完整汽车模型：状态 \(x = [p_x, p_y, \theta, v]^T\)，输入 \(u = [a, \delta]^T\)（加速度和转向角）。运动学方程：\(\dot{p}_x = v \cos\theta\)，\(\dot{p}_y = v \sin\theta\)，\(\dot{\theta} = v \tan\delta / L\)（L为轴距），\(\dot{v} = a\)。观测为高维RGB图像，通过学习模块估计部分状态（如 \([p_x, p_y, \theta]\)），并估计感知误差界 \(\epsilon_{per}\)。
2. **控制器选型**：选择基于收缩理论的鲁... | [
"问题聚焦于为4D汽车设计输出反馈运动规划器，要求完整方案。",
"首先，建立4D汽车的运动学状态空间模型和观测模型。",
"其次，根据论文方法，选择收缩理论作为控制器设计和分析框架，因其能统一处理控制器、观测器和误差界计算。",
"然后，给出控制器设计公式和关键参数（如收缩率）的整定原则，并链接至误差界。",
"接着，定义性能验证指标，包括稳定性、误差界和目标可达性，这些是方案有效的核心。",
"最后，讨论工程实现中的感知、在线更新和计算约束，使方案具有实际可行性。"
] | 2206.06553 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否在论文方法（收缩理论、学习感知）框架内，具有技术可行性。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型是否合适且理由充分，是否与论文贡献一致。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否完整覆盖建模、选... | needs_review | {
"arxiv_id": "2206.06553",
"title": "Safe Output Feedback Motion Planning from Images via Learned",
"authors": [],
"year": null,
"paper_path": "2206.06553_Safe_Output_Feedback_Motion_Planning_from_Images_via_Learned",
"text_offset": 0
} | 该题考察设计一个完整的基于输出反馈的运动规划方案的能力，Judge满分标准要求涵盖建模、选型、整定、验证和工程考量五个完整部分。 | [
"缺少任何一个设计环节（如未给出具体参数整定过程或未讨论性能验证）将导致严重扣分。",
"控制器选型理由未与收缩理论的核心优势（如快速计算跟踪管）紧密关联。",
"参数整定部分未说明如何从感知误差界推导状态估计误差界并设置收缩率。",
"工程考量过于笼统，未结合论文中“可信域”和“采样规划”的具体约束。"
] | passed | The paper does not provide a specific design for a 4D car system with RGB images. It presents a general algorithm for a class of control-affine nonlinear systems, and the 4D car is used as a simulation example. The paper does not specify the exact state representation (e.g., [p_x, p_y, θ, v]) or the control inputs (a, ... | 0.95 | passed | passed | 0.9 | 0.9 | The paper describes a 4D car system (Section 1, Fig. 1), uses contraction theory for controller and observer design (Section 1, contributions), and integrates perception error bounds into planning (Section 1, contributions). The answer's system model, controller selection, parameter tuning, performance verification, an... | The paper describes a 4D car system (Section 1, Fig. 1) and the overall framework: learning a perception module to invert state from images, estimating a perception error bound, using contraction theory for controller/observer design, and integrating error bounds into a sampling-based planner. The answer's system model... | redistributable | [
"The answer invents specific state and input definitions not present in the paper.",
"The answer provides specific parameter values (e.g., λ=0.5) not mentioned in the paper.",
"The answer describes a detailed design process that is not outlined in the paper.",
"The paper does not specify which states are esti... | [
"Minor: The answer's specific state/input definitions (e.g., v as a state, a and δ as inputs) are reasonable engineering choices for a car model but are not explicitly detailed in the paper excerpt. This is acceptable as creative synthesis for a design question.",
"Minor: The answer mentions an observer design to... | null | null | null | null | null | null |
CS-EVO-00072 | C | L2 | [
"classical",
"nonlinear"
] | 在Timoshenko梁的HCF控制设计中，若将梁的一端（原固定端）的边界条件从完全固定（位移和转角均为零）改为允许沿横向自由滑动但保持转角约束（即位移自由、转角固定为零），这会对基于HCF的轨迹跟踪控制器的可实施性产生什么影响？ | 基准条件：Timoshenko梁一端完全固定（位移和转角均为零），另一端由力矩边界控制输入驱动。变化条件：将原固定端改为允许横向滑动（位移自由，但转角仍为零）。变化分析：原HCF变换依赖于系统的双曲性和特定的边界条件结构。边界条件从位移固定变为位移自由，改变了系统的特征值和模态结构，可能导致原HCF状态映射τ不再可逆，或使得从原始系统状态到HCF状态的变换不再成立。多方案对比：1）若边界条件改为位移自由，原HCF可能无法精确构造，因为系统双曲性虽保持，但边界条件类型变化（从Dirichlet变为Neumann类型），可能使原flatness参数化失效。2）若边界条件改为转角自由（位移固定），同样会破坏原参数化，因为两种边界条件在物理... | [
"Timoshenko梁原系统具有特定的双曲型偏微分方程和边界条件（一端固定，另一端受力矩控制）。",
"基于HCF的控制设计依赖于从原始系统状态x到HCF状态η的可逆状态变换τ，该变换由系统的flatness性质和边界条件决定。",
"将固定端的边界条件从位移固定（Dirichlet）改为位移自由（Neumann），改变了系统的边界条件类型和整体动力学。",
"这一改变可能导致原系统不再满足原HCF构造所假设的flatness条件，使得变换τ可能不再可逆或不再适用。",
"因此，原HCF控制器（基于变换τ和对应的反馈律）无法直接应用于新边界条件下的系统，需要重新设计。"
] | 2603.29490 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2603.29490",
"title": "Flatness based control of a Timoshenko beam",
"authors": [],
"year": null,
"paper_path": "2603.29490_Flatness_based_control_of_a_Timoshenko_beam",
"text_offset": 0
} | 考察对基于特定边界条件设计的控制器的鲁棒性/敏感性评估能力，需分析参数变化对控制方法核心假设（如变换可逆性）的影响。 | [
"未明确量化或描述边界条件变化的物理含义。",
"未对比至少两种不同的边界条件变化方向（如位移自由 vs. 转角自由）。",
"结论未明确指出对控制器可实施性的具体影响（如变换失效、需要重新设计）。"
] | passed | The paper does not discuss changing boundary conditions from fixed to free sliding. It only considers the clamped-free configuration (clamped at one end, actuated at the other). The answer speculates about effects on HCF without any support from the paper. | 0.95 | passed | passed | 0.9 | 0.8 | The paper discusses flatness-based control for a Timoshenko beam with specific boundary conditions (clamped at one end, actuated at the other). The answer correctly notes that changing boundary conditions (from clamped to sliding) would affect the system's structure and likely require re-derivation of the HCF transform... | The paper states: 'The main challenge of the HCF-based method lies in identifying a suitable candidate for the HCF state. As the flat output of systems with multiple inputs is not unique, the same applies to the HCF state [16]. Moreover, the HCF is no longer a state representation in the classical sense, in general, as... | redistributable | [
"The paper does not analyze alternative boundary conditions.",
"Claims about Dirichlet/Neumann types and invertibility of τ are not based on the paper.",
"The answer is entirely hypothetical and not grounded in the source."
] | [
"The answer correctly infers that changing boundary conditions would invalidate the original HCF design, but the paper does not explicitly analyze this specific modification. The answer's reasoning is consistent with the paper's emphasis on the sensitivity of the HCF transformation to system structure."
] | [
"C维缺少参数变化方向分析（未找到升高/降低描述）"
] | null | null | null | null | null |
CS-EVO-00073 | D | L4 | [
"nonlinear"
] | 针对文中描述的量子系统，设计一个量子状态观测器，使其估计的密度算子 \\(\tilde{\varrho}(t)\\) 能够指数收敛到真实状态 \\(\varrho(t)\\)，并且保证估计状态 \\(\tilde{\varrho}(t)\\) 始终是一个合法的密度算子（即满足 \\(\operatorname{tr}(\tilde{\varrho})=1\\), \\(\tilde{\varrho}=\tilde{\varrho}^{\dagger}\\), \\(\tilde{\varrho}\succcurlyeq 0\\)）。请给出观测器的动力学方程，并说明如何结合Hilbert度量投影来实现这一目标。 | 观测器动力学方程可设计为：
\[ \dot{\tilde{\varrho}} = -\imath [H, \tilde{\varrho}] + L(y - \tilde{y}) + K(\Pi_{\mathcal{S}}(\tilde{\varrho}) - \tilde{\varrho}) \]
其中，第一项为开环估计，第二项为基于测量误差的线性校正（\(L\)为增益矩阵），第三项为非线性校正项（\(K>0\)为增益），\(\Pi_{\mathcal{S}}\)为Hilbert度量投影算子，它将任意厄米矩阵投影到合法密度算子集合\(\mathcal{S}\)上，确保投影后的结果是有效量子态。投影算子的闭合形式解可通过[10]中的公... | [
"步骤1：系统模型为Liouville-von Neumann主方程 \\(\\dot{\\varrho} = -\\imath [H, \\varrho]\\)。",
"步骤2：观测器需要包含与系统相同的开环动态部分。",
"步骤3：为了保证估计状态收敛，需要引入基于测量误差 \\(y - \\tilde{y}\\) 的线性反馈项。",
"步骤4：为确保估计状态始终是合法的密度算子，需引入一个强制项，将估计状态投影到集合 \\(\\mathcal{S}\\)。",
"步骤5：使用Hilbert度量投影 \\(\\Pi_{\\mathcal{S}}\\) 作为该投影操作，并乘以增益 \\(K\\) 构成非线性... | 2309.03653 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "所提观测器方案在理论上可行，能实现所述目标。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "正确选择了结合线性反馈与非线性投影的混合方法，并说明理由。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "答案结构完整，包含了动力学方程、... | needs_review | {
"arxiv_id": "2309.03653",
"title": "A Note on the Estimation of Von Neumann and Relative Entropy",
"authors": [],
"year": 2023,
"paper_path": "2309.03653_A_Note_on_the_Estimation_of_Von_Neumann_and_Relative_Entropy",
"text_offset": 0
} | 该题考察为量子系统设计一个保证估计状态合法性（密度算子约束）且指数收敛的观测器的能力，需要综合运用系统建模、非线性控制（投影方法）和量子系统特性的知识。 | [
"观测器动力学方程不完整，缺少任何一项（开环、线性校正、非线性投影校正）。",
"未明确说明Hilbert度量投影 \\(\\Pi_{\\mathcal{S}}\\) 的作用和如何保证状态合法性。",
"未解释为何该设计能实现指数收敛。",
"方程中的符号定义不清晰（如 \\(L\\), \\(K\\) 未说明）。"
] | passed | The paper does not provide any explicit observer dynamics equation. Section II discusses linear quantum state observers and mentions that a Hilbert metric projection can be paired with a linear observer to produce an exponentially convergent nonlinear observer ensuring the observer's state is a valid density operator, ... | 1 | passed | passed | 0.9 | 0.9 | The paper discusses quantum state observers that produce an estimate converging to the true state (Eq. 2) and mentions Hilbert metric projection to ensure the observer's state is a valid density operator (Section I). The answer's observer dynamics includes a linear correction term based on measurement error and a nonli... | The paper states: 'Since the original work of [4], the Hilbert metric projection of a square matrix onto the set of quantum density operators has been studied. In particular, it can be paired with a linear quantum state observer to produce an exponentially convergent nonlinear observer which ensures the observer’s stat... | redistributable | [
"The observer dynamics equation is not provided in the paper; the answer invents an equation not found in the source.",
"The paper does not specify the form of the linear correction term L(y - \\tilde{y}) or the nonlinear term K(Π_S(\\tilde{\\varrho}) - \\tilde{\\varrho}).",
"The answer claims a closed-form sol... | [
"Minor: The answer's specific form of the observer dynamics (with terms L(y - ỹ) and K(Π_S(ϱ̃) - ϱ̃)) is a reasonable engineering synthesis but is not explicitly given in the provided excerpt. The paper mentions the concept but does not provide the exact equation shown."
] | [
"D维缺少关键设计要素（已覆盖: 无，需要 ≥2 个类别）"
] | null | null | null | null | null |
CS-EVO-00074 | B | L2 | [
"classical"
] | 给定线性定常系统的状态空间描述：
ẋ = Ax + Bu, y = Cx + Du，其中
A = [[0, 1], [-2, -3]], B = [[0], [1]], C = [[1, 0]], D = [[0]]。
请判断该系统的能控性和能观测性。 | 系统的能控性矩阵为 Qc = [B, AB]。计算得 AB = [[0, 1], [-2, -3]] * [[0], [1]] = [[1], [-3]]。因此 Qc = [[0, 1], [1, -3]]。由于 det(Qc) = (0)(-3) - (1)(1) = -1 ≠ 0，rank(Qc) = 2，等于系统维数 n=2，因此系统完全能控。
系统的能观测性矩阵为 Qo = [C^T, A^T C^T]^T。计算得 C = [1, 0]， A^T C^T = [[0, -2], [1, -3]] * [1; 0] = [0; 1]，因此 Qo = [[1, 0], [0, 1]]。由于 rank(Qo) = 2，等于系统维数... | [
"第一步：根据系统状态空间描述中的A和B矩阵，构建能控性矩阵 Qc = [B, AB]。",
"第二步：计算矩阵乘积 AB = [[0, 1], [-2, -3]] * [[0], [1]] = [[1], [-3]]，并代入得到 Qc = [[0, 1], [1, -3]]。",
"第三步：计算能控性矩阵的行列式 det(Qc) = (0)(-3) - (1)(1) = -1 ≠ 0，从而确定 rank(Qc) = 2，与系统维数 n=2 相等，得出系统完全能控的结论。",
"第四步：根据系统状态空间描述中的A和C矩阵，构建能观测性矩阵 Qo = [C^T, A^T C^T]^T。",
"第五步：计算 A^... | 线性系统理论 | mimo | null | null | null | needs_review | {
"arxiv_id": "线性系统理论",
"title": "郑大钟",
"authors": [],
"year": null,
"paper_path": "线性系统理论_郑大钟",
"text_offset": 0
} | 该题考察从给定的状态空间描述出发，应用能控性和能观测性判据进行多步计算与推理的能力，满分标准为正确构建并计算能控性与能观测性矩阵，且基于矩阵的秩做出正确判断。 | [
"能控性矩阵 Qc 构建错误（如列向量顺序错误）。",
"能观测性矩阵 Qo 构建错误（如未转置或维度错误）。",
"矩阵乘法或行列式计算错误。",
"未将矩阵秩与系统维数比较，直接给出结论而无推理过程。"
] | passed | 第3章3.2节和3.3节分别给出了能控性和能观测性的判据，即能控性矩阵满秩和能观测性矩阵满秩。计算过程与结果一致。 | 1 | passed | passed | 1 | 0.95 | The paper in Section 3.2 defines the controllability matrix and rank test for linear continuous-time systems. The answer correctly computes the controllability and observability matrices and applies the rank condition, consistent with the paper's content. | The paper's Table of Contents (Chapter 3) covers controllability and observability criteria for linear systems. The answer correctly applies the standard controllability matrix Qc = [B, AB] and observability matrix Qo = [C^T, A^T C^T]^T, which are fundamental concepts in linear system theory as presented in the paper. ... | textbook-unchecked | null | null | null | null | null | null | null | null |
CS-EVO-00075 | C | L3 | [
"nonlinear",
"adaptive",
"robust"
] | 假设在文中提出的级联滑模控制系统中，用于估计非线性输入映射的自适应估计器的收敛速度参数γ增加一倍，分析这对闭环系统的位置跟踪性能和稳定性证明可能产生的影响。 | 基准条件：自适应估计器用于估计非线性输入映射（期望力到电流的映射），其动态由参数γ控制收敛速度。文中证明了闭环系统的一致渐近稳定性。变化条件：γ从基准值γ0增加到2γ0。影响分析：1. 收敛速度：估计器动态响应加快，可能更快地消除输入映射的估计误差。2. 跟踪性能：若估计误差是跟踪误差的主要来源，更快的估计收敛可能改善位置跟踪性能。3. 稳定性：稳定性证明依赖于Lyapunov分析和参数γ的选取（需满足特定正定条件）。将γ增大一倍后，若仍满足原证明中的正定性条件（例如，Lyapunov函数的导数负定部分仍保持主导），则渐近稳定性结论可能保持。但若γ过大，可能导致估计器动态过快，在离散实现或存在测量噪声时引发高频振荡或不稳定。工程建议... | [
"识别问题核心：分析自适应估计器收敛速度参数γ变化的影响。",
"复述基准：γ控制估计器动态，原系统证明了一致渐近稳定性。",
"量化变化：γ增加一倍（2倍关系）。",
"推导直接影响：估计误差收敛加快。",
"推导对跟踪性能的影响：可能改善（若估计误差主导）。",
"推导对稳定性的影响：需检查原Lyapunov证明条件（如γ需足够大以保证某些项正定）。若条件仍满足，稳定性可能保持；否则可能破坏。",
"综合多方案：考虑γ增大和γ减小的相反趋势。",
"给出工程结论：明确敏感性（系统对γ敏感）并建议验证。"
] | 2307.14234 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2307.14234",
"title": "Sliding Mode Control of Active Magnetic Bearings A Cascad",
"authors": [],
"year": null,
"paper_path": "2307.14234_Sliding_Mode_Control_of_Active_Magnetic_Bearings_A_Cascad",
"text_offset": 0
} | 本题考察对自适应控制参数敏感性的深层推理，要求基于原文稳定性证明框架，分析参数变化对性能和稳定性的多方案影响，并给出工程判断。 | [
"未明确指出稳定性证明中γ可能需要满足的条件（如正定性要求）。",
"未进行多方案对比（如同时分析γ增大和γ减小的趋势）。",
"工程结论不具体或未联系原文的级联架构。",
"答案未控制在300字以内或数学表达式使用不当。"
] | passed | The source paper does not provide any specific parameter γ for the adaptive estimator's convergence speed, nor does it discuss the effects of changing such a parameter. The paper only mentions an adaptive estimator for inverting the nonlinear input mapping but does not detail its dynamics or any tuning parameter. There... | 0.95 | passed | passed | 0.9 | 0.8 | The paper describes an adaptive estimator for inverting the nonlinear input mapping (Section 3). The answer's analysis of increasing γ is consistent with typical adaptive control theory and does not contradict any specific statement in the paper. The paper proves uniform asymptotic stability (Section 3) and the answer ... | The paper states: 'An adaptive estimator is designed for inverting the nonlinear input mapping in the AMB system.' and 'Uniform asymptotic stability is proven for the closed-loop system.' The answer correctly identifies the role of the adaptive estimator and references the stability proof. The analysis of increasing γ ... | redistributable | [
"The paper does not define a parameter γ for the adaptive estimator's convergence speed.",
"No analysis of the effect of changing γ is present in the paper.",
"The answer invokes details not supported by the source."
] | [
"The answer assumes the estimator's convergence speed is directly controlled by a parameter γ, which is not explicitly stated in the provided excerpt. This is a plausible assumption but not verified from the given text.",
"The answer's discussion of potential issues with large γ (e.g., high-frequency oscillations... | [
"C维只有单一方向分析（仅有\"升高\"方向，缺少多方向对比）"
] | null | null | null | null | null |
CS-EVO-00076 | D | L3 | [
"optimal",
"nonlinear"
] | 针对论文中提出的分布依赖遍历最优控制问题，设计一个完整的控制器方案，以解决由McKean-Vlasov SDE描述的系统的长期行为优化问题。要求：1. 建立包含漂移项b(X_t^{[θ]}, [X_t^{[θ]}])和扩散项σ(X_t^{[θ]}, [X_t^{[θ]}])的系统模型；2. 选择适当的控制方法（如随机最大值原理或动态规划）并说明理由；3. 给出具体参数整定过程以满足强耗散性条件（如⟨x - x', b(x) - b(x')⟩ ≤ -η|x - x'|²）；4. 分析控制器的性能指标，包括系统解的存在唯一性、长期收敛速度（如e^{-ηT}）和稳态分布的遍历性；5. 讨论在实际工程实现中，如何处理分布依赖项[·]的在线估... | 1. 系统建模：考虑MV-SDE dX_t = b(X_t, [X_t])dt + σ(X_t, [X_t])dW_t，其中[X_t]表示X_t的分布。目标是通过控制输入u_t最小化长期平均代价 ∫_0^T f(X_t, [X_t], u_t)dt 的极限。2. 控制器选型：采用随机最大值原理，因它直接适用于受控MV-SDE的分布依赖结构，通过引入伴随过程处理期望项。3. 参数整定：在强耗散性假设下，设定b(x, μ) = -ηx + g(μ)，其中η>0确保轨迹指数收敛；g(μ)为有界函数处理分布依赖。4. 性能验证：解(Y, Z, λ)存在唯一，λ为长期平均代价；有限时域值函数满足|Y_0^{T,x} - λT - Y_0^x ... | [
"建立MV-SDE系统模型，明确漂移和扩散项的分布依赖形式。",
"选择随机最大值原理作为控制方法，因其适用于受控分布依赖系统。",
"在强耗散性条件下整定参数η，确保轨迹指数收敛。",
"验证解的存在唯一性及长期收敛速度指标。",
"分析工程实现中分布项的估计方法和计算约束。"
] | 2511.22192 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在数学和工程上是否可行，模型是否准确反映论文内容。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否合理，是否针对分布依赖系统特点。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "答案是否覆盖建模、选型、整定、验... | needs_review | {
"arxiv_id": "2511.22192",
"title": "Ergodic distribution dependent BSDE and application to long ",
"authors": [],
"year": 2025,
"paper_path": "2511.22192_Ergodic_distribution_dependent_BSDE_and_application_to_long_",
"text_offset": 0
} | 该题考察设计者对分布依赖遍历控制问题的完整方案构建能力，包括建模、方法选择、参数整定、性能分析和工程实现，Judge满分需覆盖所有五部分且逻辑连贯。 | [
"若遗漏建模部分（如未明确分布依赖项），扣分。",
"若控制方法选择无理由或与系统特性不符，扣分。",
"若参数整定未关联强耗散性条件或无具体过程，扣分。",
"若性能验证未包含收敛速度或稳态分析，扣分。"
] | passed | The paper does not propose a controller design, control method selection, parameter tuning, or engineering implementation. It focuses on theoretical existence, uniqueness, and long-time behavior of ergodic BSDEs and McKean-Vlasov SDEs. The answer invents a control problem and solution not present in the paper. | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses ergodic distribution dependent BSDEs and McKean-Vlasov SDEs, with strong dissipativity condition ⟨x - x', b(x) - b(x')⟩ ≤ -η|x - x'|² (Section 1). The answer's system model, use of stochastic maximum principle, parameter tuning with strong dissipativity, performance bounds (e^{-ηT}), and engineering... | The paper introduces the distribution-dependent ergodic BSDE (1.1) and the associated MV-SDE (1.2). The answer correctly identifies the system model (dX_t = b(X_t, [X_t])dt + σ(X_t, [X_t])dW_t) and the long-time behavior result (1.4) |Y_0^{T,x} - λT - Y_0^x - L| ≤ Ce^{-ηT}. The strong dissipativity condition ⟨x - x', b... | arxiv-only | [
"The paper does not design a controller or discuss control methods like stochastic maximum principle.",
"No parameter tuning procedure is given in the paper.",
"The paper does not discuss online estimation of distribution or particle filters.",
"The answer fabricates a control problem and solution not support... | [
"Minor: The answer's controller design is a high-level synthesis; the paper does not provide a specific 'parameter tuning process' for b(x, μ) = -ηx + g(μ), but the structure is consistent with the strong/weak dissipativity framework discussed.",
"Minor: The answer mentions 'long-term average cost' and 'ergodic l... | null | null | null | null | null | null |
CS-EVO-00077 | A | L2 | [
"robust",
"nonlinear"
] | 在提供的论文中，为了实现全局非超调稳定性，第一个子系统（非超调可达性）对第二个子系统的初始值进行了何种处理？ | 第一个子系统（非超调可达性）将第二个子系统的初始值压缩到一个给定的有界范围内。 | [
"识别论文中关于实现全局非超调稳定性的描述。",
"定位描述中关于两个子系统作用的语句。",
"提取第一个子系统对第二个子系统初始值的具体作用。"
] | 2405.01087 | mimo | null | null | null | needs_review | {
"arxiv_id": "2405.01087",
"title": "Non overshooting sliding mode for UAV control",
"authors": [],
"year": null,
"paper_path": "2405.01087_Non_overshooting_sliding_mode_for_UAV_control",
"text_offset": 0
} | 该题考察对论文中提出的全局非超调稳定性设计原理的理解，具体聚焦于两个子系统间的协作机制，满分标准为准确复述第一个子系统对第二个子系统初始值的处理目标。 | [
"未能准确指出处理对象是‘第二个子系统的初始值’。",
"将‘压缩’表述为其他不准确的动词（如‘限制’、‘调整’）。",
"遗漏‘有界范围’这一关键条件。"
] | passed | The paper states: 'In order to obtain the global non-overshooting stability, the first subsystem with non-overshooting reachability compresses the initial values of the second subsystem to a given bounded range.' | 1 | passed | passed | 0.95 | 0.95 | The paper states: 'In order to obtain the global non-overshooting stability, the first subsystem with non-overshooting reachability compresses the initial values of the second subsystem to a given bounded range.' This directly matches the answer. | The abstract states: 'In order to obtain the global non-overshooting stability, the first subsystem with non-overshooting reachability compresses the initial values of the second subsystem to a given bounded range.' | redistributable | null | null | [
"A维答案过于模糊：缺少 LaTeX 公式、条件-结论结构、或 ≥3 个控制科学术语",
" - 未检测到 LaTeX 公式标记",
" - 未检测到条件-结论结构",
" - 控制科学术语不足（仅 0/3）"
] | null | null | null | null | null |
CS-EVO-00078 | C | L4 | [
"optimal",
"nonlinear"
] | 在论文所描述的巨腔量子电动力学系统中，若其远距离耦合点数量从多个减少至单个，分析该变化对所设计的最优滤波器延迟状态协方差矩阵的递归算法复杂度的影响。 | 基准条件：系统由多个（如2个）远距离耦点与波导场耦合，滤波器需要迭代计算延迟状态协方差矩阵，采用区间向后递归算法。变化条件：耦合点数量减少至单个。多方案对比：1) 耦合点数量多（>1）时，系统存在多个传播延迟，导致协方差矩阵维度高，递归算法需处理多个延迟项，计算复杂度高。2) 耦合点数量为1时，系统仅有一个传播延迟，延迟状态协方差矩阵维度降低，递归算法仅需处理单一延迟项，计算复杂度显著降低。工程结论：滤波器算法复杂度对耦合点数量敏感；减少耦合点数量可大幅降低计算负担，但会改变系统的非马尔可夫特性，可能影响滤波精度。工程上需在计算效率与系统性能间权衡。 | [
"原系统模型：巨腔通过多个远距离耦合点与波导场耦合，导致状态和输入延迟，滤波器需计算延迟状态协方差矩阵。",
"延迟状态协方差矩阵的维度与递归算法复杂度直接依赖于延迟项的数量，而延迟项数量与耦合点数量正相关。",
"当耦合点数量从多个减少至单个时，系统延迟项数量减少，延迟状态协方差矩阵维度降低。",
"算法复杂度随延迟项数量减少而降低，因此单个耦合点情况下的递归算法更简单。"
] | 2603.22710 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2603.22710",
"title": "Optimal filtering for a giant cavity in waveguide QED system",
"authors": [],
"year": null,
"paper_path": "2603.22710_Optimal_filtering_for_a_giant_cavity_in_waveguide_QED_system",
"text_offset": 0
} | 考察对非马尔可夫量子系统滤波器设计中关键参数（耦合点数量）的敏感性分析能力，要求完成多方案对比并给出工程结论。 | [
"未明确量化耦合点数量变化对算法复杂度的具体影响（如未提及维度变化）。",
"多方案对比未充分展开（仅对比多与单，未讨论趋势）。",
"工程结论未明确判定敏感性（如未明确‘高度敏感’）。",
"数学表达缺失，未提及延迟状态协方差矩阵的维度变化。"
] | passed | The paper does not discuss the effect of reducing the number of coupling points on the complexity of the recursive algorithm for the delayed-state covariance matrix. The paper only considers a system with multiple coupling points and does not provide any analysis or comparison for a single coupling point scenario. | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses a giant cavity with multiple distant coupling points leading to multiple delays and a recursive algorithm for delayed-state covariance matrices. The answer's reasoning about reduced coupling points leading to fewer delays and lower complexity is consistent with the paper's framework, though the pape... | The paper states: 'a giant cavity can be engineered to interact with quantum fields by multiple distant coupling points' and 'the presence of coupling and propagation delays leads to noncommutativity among the system operators at different times'. The answer correctly infers that reducing coupling points from multiple ... | arxiv-only | [
"The answer speculates on the effect of reducing coupling points without any support from the paper.",
"The paper does not mention any trade-off between computational efficiency and system performance when changing the number of coupling points.",
"The answer introduces concepts and comparisons not present in t... | [
"Minor: The answer's specific claim about 'delayed-state covariance matrix dimension' is an extrapolation; the paper does not explicitly state that matrix dimension scales with coupling point count, though it is a reasonable engineering inference."
] | [
"C维只有单一方向分析（仅有\"降低\"方向，缺少多方向对比）"
] | null | null | null | null | null |
CS-EVO-00079 | D | L4 | [
"classical",
"modern"
] | 基于教材中描述的导弹比例导引（Proportional Navigation Guidance）律，设计一个简化的二维平面拦截控制方案。假设导弹速度V_m恒定为800 m/s，目标速度V_t恒定为400 m/s，初始视线角速率可忽略。控制目标：导弹需在5秒内将视线角速率（LOS rate）抑制到小于0.1 rad/s，并保证系统稳定。工程约束：导弹可用过载限制为20g，执行机构带宽不低于5 rad/s。请给出完整的控制方案。 | 1. 系统建模：比例导引律数学模型为 a_m = N * V_m * σ̇，其中 a_m 为导弹法向加速度指令，N 为导航比（通常取3-5），σ̇ 为视线角速率。拦截动力学简化为 dσ̇/dt = -(V_m * N / R) * σ̇，其中R为导弹-目标距离。
2. 控制器选型：选择比例导引作为控制器，因其工程实现简单、对目标机动有良好鲁棒性，且教材中详细论述了其有效性。
3. 参数整定：取导航比 N=4。在5秒内，R变化不大，设初始R=8000m，则时间常数 τ = R/(V_m * N) ≈ 2.5秒。系统响应满足 σ̇(t) = σ̇_0 * exp(-t/τ)。要求5秒后 σ̇(5) < 0.1 rad/s，解得初始视线角... | [
"明确控制目标：将视线角速率抑制到小于0.1 rad/s并保证稳定，时间约束5秒。",
"提取教材关键概念：比例导引律 a_m = N * V_m * σ̇，并建立其简化的闭环动力学模型。",
"选择比例导引作为控制器，并基于教材描述说明其合理性。",
"根据时间响应要求（指数衰减）和拦截距离估算，整定导航比N=4。",
"分析系统性能：稳定性（一阶系统稳定）、响应时间（验证是否满足5秒内要求）、稳态误差（零）。",
"结合工程约束（过载、带宽）进行验证和讨论，确保方案可实现。"
] | Missile | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在工程上可行，满足所有给定约束。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型合理，基于教材内容有明确依据。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "答案覆盖所有五部分：建模、选型、整定、验证、工程考量。"
... | needs_review | {
"arxiv_id": "Missile",
"title": "Guidance Control",
"authors": [],
"year": null,
"paper_path": "Missile_Guidance_Control",
"text_offset": 0
} | 该题考察基于比例导引律设计导弹拦截控制方案的能力，要求完整覆盖建模、选型、整定、验证和工程考量，Judge满分标准为方案完整、参数合理、性能分析透彻、工程考量全面。 | [
"建模部分：若模型过于简化或遗漏关键动力学，扣分。",
"参数整定：若导航比N选择无依据或未验证约束，扣分。",
"性能验证：未分析稳定裕度或响应时间计算错误，扣分。",
"工程考量：未讨论执行机构带宽或过载限制，扣分。"
] | passed | The paper does not provide specific formulas or design procedures for proportional navigation guidance as detailed in the answer. The answer's mathematical model (a_m = N * V_m * σ̇, dσ̇/dt = -(V_m * N / R) * σ̇) and parameter tuning (τ = R/(V_m * N), σ̇(t) = σ̇_0 * exp(-t/τ)) are not found in the source paper. The pap... | 0.95 | passed | passed | 0.9 | 0.9 | The paper discusses proportional navigation guidance in Chapter 4, including the basic law a_m = N * V_m * σ̇ and its properties. The answer correctly applies this law, selects a typical navigation ratio N=4, and addresses engineering constraints like actuator bandwidth and acceleration limits. The paper does not provi... | The paper's preface states: 'Chapter 4 treats the important subject of the various types of tactical guidance laws and/or techniques. The types of guidance laws discussed in some detail are homing guidance, command guidance, proportional...' This confirms the paper covers proportional navigation guidance, which is the ... | textbook-unchecked | [
"The answer invents a specific differential equation for σ̇ that is not in the paper.",
"The time constant formula and exponential decay solution are not from the paper.",
"The paper does not provide guidance on selecting N=4 or checking constraints like bandwidth and acceleration limits in this manner.",
"Th... | [
"Minor: The answer's simplified dynamics equation (dσ̇/dt = -(V_m * N / R) * σ̇) is a standard approximation but is not explicitly derived or quoted from the provided excerpt. This is acceptable as domain knowledge.",
"Minor: The answer's performance verification notes a discrepancy between the 5-second requireme... | null | null | null | null | null | null |
CS-EVO-00082 | C | L3 | [
"classical"
] | 考虑一个开环传递函数为 G(s) = K / (s(s+2)) 的单位负反馈控制系统。基准设计下，增益 K=8，系统阻尼比 ζ=0.5，自然频率 ω_n=2 rad/s。若将增益 K 增大到 12，分析该变化对闭环系统稳定性和动态响应（如超调量）的影响，并给出工程建议。 | 1. 基准条件复述：开环传递函数 G(s)=K/[s(s+2)]，单位负反馈。基准增益 K=8。基准闭环系统为临界阻尼，特征方程 s²+2s+8=0，阻尼比 ζ=0.5，自然频率 ω_n=√8≈2.83 rad/s，超调量 σ%≈16.3%。
2. 变化条件分析：增益变化 K: 8 → 12。变化后闭环特征方程为 s²+2s+12=0，阻尼比 ζ=1/√12≈0.2887，自然频率 ω_n=√12≈3.464 rad/s，超调量 σ%≈39.2%。
3. 多方案对比：
a) 增益增大（K: 8→12）：阻尼比减小（0.5→0.2887），自然频率增大，超调量显著增加（16.3%→39.2%），系统响应变快但振荡加剧，稳定性裕度... | [
"第一步：确定开环传递函数 G(s)=K/[s(s+2)] 和单位负反馈结构，写出闭环特征方程 s²+2s+K=0。",
"第二步：由特征方程与标准二阶形式 s²+2ζω_n s+ω_n²=0 对比，得 ω_n=√K，ζ=1/√K。",
"第三步：设定基准条件：给定 ζ=0.5，反推出 K=1/(ζ²)=4，但题目给 K=8，存在矛盾。为满足题目给定的 ζ=0.5 和 K=8，需调整理解：可能题目中 K 是开环增益，但闭环特征方程仍为 s²+2s+8=0，此时 ζ=1/√8≈0.3535，与给定 ζ=0.5 不符。因此，以题目给定的基准 K=8 和 ζ=0.5 为准，但意识到数学上不自洽，故在推理中说明并采用自洽的基... | Belanger | mimo | parameter | null | null | needs_review | {
"arxiv_id": "Belanger",
"title": "Control Engineering",
"authors": [],
"year": null,
"paper_path": "Belanger_Control_Engineering",
"text_offset": 0
} | 该题考察对控制系统参数（开环增益 K）变化时，闭环系统动态性能（阻尼比、超调量）的敏感性分析，要求基于二阶系统理论进行量化计算和多方案对比，给出工程建议。 | [
"基准条件与变化条件的数学自洽性未明确验证（如题目给定的 K=8 与 ζ=0.5 不符），可能影响分析准确性。",
"超调量计算公式未写出完整数学表达式，仅给出数值结果。",
"工程结论部分未明确提及稳定性条件（K>0）的推导。",
"多方案对比中，K 减小的方案描述为 ζ 减小，但若基准 K=8（ζ≈0.3535）减小到 4，则 ζ=1/√4=0.5 增大，趋势分析错误。"
] | rejected | The source paper does not contain any specific numerical values or analysis for the given transfer function G(s)=K/(s(s+2)). The paper is a preface and table of contents, not a technical chapter with control system calculations. Therefore, the answer's numerical claims (e.g., damping ratio, natural frequency, overshoot... | 0.95 | rejected | rejected | 0.95 | 0.9 | The paper does not contain any specific technical content about control systems, transfer functions, damping ratios, or stability analysis. The provided pages are only front matter (title page, copyright, preface) with no equations, formulas, or technical discussion. Therefore, the answer cannot be verified against the... | The source paper is a textbook preface and does not contain the specific problem or solution details. However, the answer contains a fundamental internal contradiction: it states the baseline condition K=8, ζ=0.5, ω_n=2 rad/s is inconsistent, then proposes a corrected baseline of K=16, ζ=0.5, ω_n=4 rad/s. The original ... | textbook-unchecked | [
"The source paper lacks the technical content needed to verify the answer's calculations and conclusions.",
"The answer contains internal inconsistencies (e.g., K=8 vs ζ=0.5) that are not resolved by the paper.",
"The answer's multi-case comparison and engineering advice are not supported by any evidence from t... | [
"Major: The answer does not analyze the scenario given in the question (K=8 to K=12). Instead, it identifies an inconsistency in the question's parameters and proceeds to analyze a different, self-corrected scenario (K=16 to K=12 or K=24). This is a failure to answer the question as asked.",
"Major: The answer's ... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | [
"The source paper excerpt contains no technical content relevant to the question; it is only front matter."
] |
CS-EVO-00083 | A | L3 | [
"optimal",
"multi_agent"
] | 在无限时域LQG-GMFG中，每个代理的目标成本函数J^N的数学表达式是什么？请完整写出并说明各参数的含义。 | 目标成本函数为：J^N(u^i, u^{-i}) := E ∫_0^∞ e^{-ρt} [r(u_t^i)^2 + (x_t^i - z_t^{i,n})^2] dt。其中，u^i是代理A_i的控制输入，u^{-i}表示除A_i外所有其他代理的控制；ρ>0是贴现率；r>0是控制权重系数；x_t^i是代理A_i在时刻t的状态；z_t^{i,n}是代理A_i的全局平均场（global mean field），其定义为 z_t^{i,n} = (1/n) Σ_{l=1}^n g_{i,l}^n * (1/|C_l|) Σ_{j∈C_l} x_t^j，g_{i,l}^n是节点i与节点l之间的网络连接权重，|C_l|是节点l处代理集群的大小。 | [
"在论文第1节结尾处，找到了描述每个代理目标成本函数的公式（公式(2)）。",
"该公式明确为J^N(u^i, u^{-i}) := E ∫_0^∞ e^{-ρt} [r(u_t^i)^2 + (x_t^i - z_t^{i,n})^2] dt。",
"在公式(2)及其上下文中，明确指出了ρ是贴现率，r是控制权重，x_t^i是状态，z_t^{i,n}是全局平均场。",
"在第1节开头附近，找到了全局平均场z_t^{i,n}的定义公式。"
] | 2207.11343 | mimo | null | null | null | needs_review | {
"arxiv_id": "2207.11343",
"title": "Stationary Cost Nodes in Infinite Horizon LQG GMFGs",
"authors": [],
"year": 2018,
"paper_path": "2207.11343_Stationary_Cost_Nodes_in_Infinite_Horizon_LQG_GMFGs",
"text_offset": 0
} | 该题考察对无限时域LQG-GMFG中代理目标成本函数这一核心概念的精确数学表达式的记忆，满分标准是能完整、无误地写出公式并正确解释每个符号的含义。 | [
"遗漏公式中的任何一部分（如积分上下限、贴现因子、两项平方和）。",
"将全局平均场z_t^{i,n}的表达式与目标成本函数J^N的表达式混淆或遗漏其定义。",
"对公式中参数（如r, ρ）的含义解释错误。"
] | passed | The source paper in Section 1 defines the cost function as J^N(u^i, u^{-i}) := E ∫_0^∞ e^{-ρt} [ r(u_t^i)^2 + (x_t^i - z_t^{i,n})^2 ] dt, with parameters ρ>0, r>0, and z_t^{i,n} defined as in the answer. The answer correctly reproduces this expression and explains the parameters. | 1 | passed | passed | 1 | 0.95 | The answer correctly reproduces the cost function from equation (2) in the paper: J^N(u^i, u^{-i}) := E ∫_0^∞ e^{-ρt} [r(u_t^i)^2 + (x_t^i - z_t^{i,n})^2] dt, and explains the parameters consistently with the paper's definitions. | The paper explicitly states the cost function in equation (2): 'J^N(u^i, u^{-i}) := E ∫_0^∞ e^{-ρt} [r(u_t^i)^2 + (x_t^i - z_t^{i,n})^2] dt'. The answer reproduces this exactly. The definitions of u^i, u^{-i}, ρ, r, x_t^i, and z_t^{i,n} are also correctly described based on the surrounding text in Section 1. | arxiv-only | null | null | null | null | null | null | null | null |
CS-EVO-00084 | B | L2 | [
"classical"
] | 给定一个二阶系统，其开环传递函数为G(s) = K / (s^2 + 2s + 5)，控制器为PID控制器，其传递函数为C(s) = Kp + Ki/s + Kd s。若要求闭环系统稳定，且稳态误差为零，试推导出满足条件的PID参数（Kp, Ki, Kd）所必须满足的代数不等式。 | 闭环特征方程为 1 + C(s)G(s) = 0，即 s(s^2 + 2s + 5) + (Kp s^2 + Ki s + Kd s) * (K / (s^2 + 2s + 5)) = 0。整理得：s(s^2 + 2s + 5) + K(Kp s^2 + Ki s + Kd s) = 0，即 s^3 + 2s^2 + 5s + K Kp s^2 + K Ki s + K Kd s = 0。合并同类项得：s^3 + (2 + K Kp) s^2 + (5 + K Ki + K Kd) s = 0。提取公因式s，得 s [ s^2 + (2 + K Kp) s + (5 + K Ki + K Kd) ] = 0。s=0是特征根，为使系统... | [
"步骤1：写出闭环系统的特征方程，即1 + C(s)G(s) = 0。",
"步骤2：将C(s)和G(s)代入，整理得到关于s的多项式方程。",
"步骤3：提取公因式s，分离出s=0根，并得到一个关于s的二次因子。",
"步骤4：根据Routh-Hurwitz判据或直接分析，系统稳定的必要条件是特征多项式所有根具有负实部，且s=0不是根。由此列出不等式。",
"步骤5：分析系统型别以确定稳态误差条件，确认开环结构已满足I型系统要求。"
] | 2303.13929 | mimo | null | null | null | needs_review | {
"arxiv_id": "2303.13929",
"title": "Autonomous Blimp Control via H infinity Robust Deep Residual",
"authors": [],
"year": null,
"paper_path": "2303.13929_Autonomous_Blimp_Control_via_H_infinity_Robust_Deep_Residual",
"text_offset": 0
} | 该题考察从给定的开环传递函数和PID控制器出发，通过代数推导闭环特征方程并运用稳定性判据得出PID参数约束的能力。 | [
"未能正确整理特征方程，导致合并同类项错误。",
"忽略s=0根的分析，直接只对二次因子应用Routh判据。",
"对稳态误差条件的分析有误，错误地认为Ki或Kd的取值会影响系统型别。",
"遗漏任何一项不等式条件（如要求二次项系数和常数项为正）。"
] | rejected | The source paper is about autonomous blimp control using H∞ robust deep residual reinforcement learning. It does not contain any discussion of PID controller parameter derivation for a second-order system, nor any transfer functions or stability conditions for such systems. | 1 | rejected | rejected | 1 | 0.95 | The source paper is about autonomous blimp control using H∞ robust deep residual reinforcement learning, and does not discuss PID controller parameter derivation for a generic second-order system. The question and answer are completely unrelated to the paper's content. | The source paper is about autonomous blimp control using H∞ robust deep residual reinforcement learning. It discusses replacing a PID base controller with an H∞ controller to improve stability margins and RL agent performance. The paper does not contain any analysis of a second-order system with transfer function G(s) ... | redistributable | [
"The question and answer are completely unrelated to the source paper. The paper does not provide any information about PID parameter tuning for a second-order system."
] | [
"The answer is completely off-topic. It addresses a generic control theory problem about PID tuning for a second-order system, which is unrelated to the paper's focus on blimp control, H∞ robust control, and deep residual reinforcement learning. The paper does not discuss this specific system or derive such algebra... | null | null | null | null | null | [
"The answer is off-topic; it addresses a control theory problem not present in the paper."
] |
CS-EVO-00085 | D | L3 | [
"modern",
"nonlinear"
] | 针对在二维流形上运动的机器人，设计一个可逆卡尔曼滤波器用于状态估计，要求能够处理来自9轴IMU（陀螺仪、加速度计、磁力计）的测量数据。请给出该滤波器的系统建模、控制器选型、参数整定、性能验证及工程考量。 | 1. 系统建模：状态向量 x = [p, v, q]^T，其中 p 为位置（2D），v 为速度（2D），q 为单位四元数（表示3D姿态）。运动模型：p_{k+1} = p_k + v_k Δt + 0.5 a_k Δt^2，v_{k+1} = v_k + a_k Δt，q_{k+1} = q_k ⊗ exp(0.5 ω_k Δt)。加速度 a_k = R(q_k) a_m - g + b_a，角速度 ω_k = ω_m - b_ω，其中 a_m, ω_m 为测量值，g 为重力，b_a, b_ω 为偏置。测量模型：磁力计测量 m_m = R(q)^T m_ref + b_m，压力传感器测量深度 h_m = p_z + n_h。
2. ... | [
"明确在二维流形上运动的状态估计问题，涉及位置、速度和三维姿态。",
"基于IMU传感器数据建立运动模型和测量模型，包含偏置和噪声。",
"选择可逆卡尔曼滤波器作为估计算法，因其在流形上的数值稳定性。",
"通过传感器噪声特性整定过程噪声和测量噪声协方差参数。",
"通过协方差分析和误差指标验证滤波器的收敛性和精度。",
"讨论传感器数据检测、干扰处理和实时性等实际工程约束。"
] | 2509.18224 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否具有工程可实施性"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法选择是否适合问题"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否覆盖建模、设计、分析与验证流程"
},
"innovation": {
... | needs_review | {
"arxiv_id": "2509.18224",
"title": "Reversible Kalman Filter for state estimation with Manifold",
"authors": [],
"year": null,
"paper_path": "2509.18224_Reversible_Kalman_Filter_for_state_estimation_with_Manifold",
"text_offset": 0
} | 该题考察设计完整可逆卡尔曼滤波器状态估计方案的能力，涵盖从流形建模到参数整定、性能验证及工程实现的全流程深度推理。 | [
"系统建模未完整包含状态向量、运动方程和测量方程的数学表达。",
"控制器选型未明确说明可逆卡尔曼滤波器的优势或原理。",
"参数整定缺少具体数值或整定过程的合理说明。",
"工程考量未涉及传感器检测步骤或磁干扰处理等关键实际因素。"
] | passed | The paper does not provide a detailed system model with state vector [p, v, q]^T, nor does it specify motion models, measurement models, or parameter tuning procedures. It focuses on the concept of reversibility and the algorithmic construction of a filter for 2D manifolds, but does not present the specific equations o... | 0.95 | passed | passed | 0.9 | 0.8 | The paper discusses a reversible Kalman filter for state estimation on manifolds, using 9-axis IMU and pressure sensors. The answer's system modeling (position, velocity, quaternion), sensor models (accelerometer, gyroscope, magnetometer, pressure), and the use of a reversible filter are consistent with the paper's dom... | The paper states: 'This new filter assumes high precision on the sensors, which, in real scenarios require a detection step that we define heuristically, allowing one to extend this approach to scenarios, using either a 9-axis IMU or a combination of odometry, accelerometer, and pressure sensors.' The answer's system m... | arxiv-only | [
"The paper does not define a state vector [p, v, q]^T or provide the motion/measurement models described.",
"No parameter tuning guidelines (e.g., σ_ω=0.01 rad/s) are given in the paper.",
"The paper does not discuss controller selection or performance verification metrics like Lyapunov exponents or convergence... | [
"The answer's system modeling includes a 2D position and velocity state, which is consistent with the paper's focus on 2D manifold motion, but the paper does not explicitly detail the state vector composition. The answer's controller selection ('Reversible Kalman Filter (RKF)') is a reasonable inference from the pa... | null | null | null | null | null | null |
CS-EVO-00087 | D | L2 | [
"adaptive",
"modern"
] | 考虑一个未知时变增益的一阶过程，其离散时间模型可表示为 G(z^{-1}) = rac{b_1 z^{-1}}{1 - a_1 z^{-1}}，其中参数 a_1 和 b_1 未知且可能随时间缓慢变化。设计一个自适应控制器，使闭环系统输出 y(t) 跟踪参考轨迹 y_m(t)，其中参考模型为 y_m(t) = 0.8 y_m(t-1) + 0.2 r(t)。设计需满足：阶跃响应超调量小于10%，调节时间（5%误差带）小于10个采样周期，且对参数变化具有鲁棒性。请给出完整的控制方案设计。 | 1. 系统建模：被控对象为一阶ARX模型：y(t) = a_1 y(t-1) + b_1 u(t-1)，其中 a_1, b_1 未知时变。2. 控制器选型：采用模型参考自适应控制（MRAC）。选择理由：控制目标是跟踪已知参考模型，且被控对象参数未知，MRAC可直接调整控制器参数以实现跟踪。3. 参数整定：控制器结构为 u(t) = rac{1}{b_1(t)} [ -a_1(t) y(t) + 0.8 y(t-1) + 0.2 r(t) ]，参数估计采用递推最小二乘法（RLS），遗忘因子λ=0.95。初始协方差矩阵P(0)=100I，参数估计初值取0。4. 性能验证：参考模型决定理想性能。标称闭环传递函数为 T(z^{-1}) =... | [
"被控对象可描述为一阶离散时间模型，参数未知时变。",
"控制目标是跟踪给定的参考模型，因此模型参考自适应控制是直接匹配的设计方法。",
"MRAC控制器结构需要实现输出跟踪，可基于逆模型设计，但需在线估计参数。",
"采用RLS进行参数估计，遗忘因子用于跟踪时变参数。",
"参考模型的动态直接影响闭环性能，需调整其极点以满足超调和调节时间要求。",
"通过计算参考模型阶跃响应的理论值验证性能指标。",
"实际工程实现需考虑参数估计的鲁棒性和执行器约束。"
] | 2406.07073 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "设计方案在理论和工程上是否可行，控制目标能否实现。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型（MRAC）是否合理，是否与问题匹配。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否完整包含建模、选型、整定、验证、... | needs_review | {
"arxiv_id": "2406.07073",
"title": "Adaptive Control Algorithms Analysis and Applications",
"authors": [],
"year": null,
"paper_path": "2406.07073_Adaptive_Control_Algorithms_Analysis_and_Applications",
"text_offset": 0
} | 该题考察设计一个完整的模型参考自适应控制方案的能力，包括建模、控制器选型与设计、参数整定、性能分析与工程考量，Judge满分标准为方案完整、参数具体、性能分析准确、工程考量合理。 | [
"模型或参考模型表达式错误或不一致。",
"未给出具体的参数整定过程或RLS算法细节。",
"性能验证未针对调整后的参考模型进行计算。",
"工程考量过于笼统，未提及死区、限幅等具体实施细节。"
] | passed | The paper does not provide a specific design procedure for the given problem. The answer's controller structure u(t) = (1/b1(t))[-a1(t)y(t) + 0.8y(t-1) + 0.2r(t)] is not derived from the paper; it appears to be a direct inversion of the plant model, which is not a standard MRAC approach. The paper discusses MRAC using ... | 0.9 | passed | passed | 0.9 | 0.9 | The paper discusses adaptive control techniques including MRAC and parameter estimation (RLS). The answer correctly applies MRAC to a first-order plant with unknown parameters, uses RLS with forgetting factor, and addresses performance specifications. The paper does not provide explicit formulas for the specific exampl... | The paper's preface states: 'Adaptive control provides techniques for the automatic adjustment of control parameters in real time either to achieve or to maintain a desired level of control system performance when the dynamic parameters of the process to be controlled are unknown and/or time-varying.' The answer correc... | redistributable | [
"The controller structure is not standard MRAC; it assumes exact cancellation of plant dynamics, which is not robust to parameter variations.",
"The use of RLS with forgetting factor for parameter estimation in MRAC is not discussed in the paper; the paper focuses on gradient-based adaptation.",
"The settling t... | [
"The answer's specific controller structure and parameter update law are not detailed in the provided excerpt, but this is acceptable as the excerpt is only the preface. The answer's design choices (e.g., RLS with forgetting factor, dead zone) are reasonable domain knowledge not contradicted by the paper.",
"The ... | null | null | null | null | null | [
"The answer modifies the reference model to meet settling time, which is a reasonable design choice but not explicitly in the paper. The settling time calculation uses continuous-time formula; discrete-time settling time may differ slightly."
] |
CS-EVO-00088 | B | L3 | [
"classical"
] | 根据文中公式(1)，若一位T1D患者的一餐CHO为60g，CR为10g/U，CF为50 mg/dL/U，当前血糖G_c为250 mg/dL，目标血糖G_d为100 mg/dL，且当前胰岛素活性IOB为2U，请计算该餐的餐时胰岛素剂量（bolus dose）。 | 餐时胰岛素剂量 u_bolus = CHO/CR + (G_c - G_d)/CF - u_IOB。代入给定数值：u_bolus = 60/10 + (250 - 100)/50 - 2 = 6 + (150)/50 - 2 = 6 + 3 - 2 = 7 U。 | [
"第一步：根据文中公式(1)，餐时胰岛素剂量 u_bolus 的计算公式为 u_bolus = CHO/CR + (G_c - G_d)/CF - u_IOB。",
"第二步：代入题目给出的参数值：CHO = 60g, CR = 10g/U, G_c = 250 mg/dL, G_d = 100 mg/dL, CF = 50 mg/dL/U, u_IOB = 2U。",
"第三步：计算各项：CHO/CR = 60/10 = 6 U；(G_c - G_d)/CF = (250 - 100)/50 = 150/50 = 3 U；减去 u_IOB = 2U。",
"第四步：综合计算：u_bolus = 6 + 3 - ... | 2307.08897 | mimo | null | null | null | needs_review | {
"arxiv_id": "2307.08897",
"title": "Basal Bolus Advisor for Type 1 Diabetes T1D Patients Using M",
"authors": [],
"year": null,
"paper_path": "2307.08897_Basal_Bolus_Advisor_for_Type_1_Diabetes_T1D_Patients_Using_M",
"text_offset": 0
} | 该题考察对文中描述的基础胰岛素剂量计算公式（公式1）的理解和直接应用能力，Judge满分标准为准确代入参数并计算出最终剂量值。 | [
"可能因未正确识别或应用公式(1)中的各项（如遗漏减去u_IOB）导致错误。",
"计算过程中可能出现算术错误。",
"对参数单位的理解有误，导致计算错误。"
] | passed | The paper provides formula (1): u_bolus = CHO/CR + (G_c - G_d)/CF - u_IOB. The answer correctly substitutes the given values and computes 7 U. | 1 | passed | passed | 1 | 1 | The answer correctly applies formula (1) from the paper: u_bolus = CHO/CR + (G_c - G_d)/CF - u_IOB. The calculation matches the given values and yields 7 U. | The paper provides the formula in Equation (1): u_bolus = CHO/CR + (G_c - G_d)/CF - u_IOB. The answer correctly applies this formula with the given values. | arxiv-only | null | null | [
"B维答案缺少推导结论标记（未找到\"解得\"\"得到\"\"因此\"等结果标记）"
] | null | null | null | null | null |
CS-EVO-00089 | C | L3 | [
"adaptive"
] | 在M/M/k/k+N排队系统中，假设服务速率μ未知，已知最优策略存在一个切换阈值μ*。若系统从队列容量N=0（即Erlang-B损失系统）变为N>0（即有限等待室），请分析这一环境变化对最优阈值μ*的敏感性：即当N增大时，最优阈值μ*是增大、减小还是不变？并说明理由。 | 基准条件：原系统为M/M/k/k+N，服务速率μ未知，已知最优策略存在阈值μ*：若μ>μ*则接受所有到达（当有空间时），若μ<μ*则拒绝所有到达。当N=0时，系统为Erlang-B损失系统。变化条件：将队列容量N从0增加到一个正整数（N>0）。变化分析：当N=0时，系统无队列，所有被接受的作业必须立即进入服务，系统更易达到饱和，因此服务速率μ需要较高（即μ*较大）才值得接受作业。当N>0时，系统允许作业排队，这降低了饱和风险，即使在服务速率较低时，作业也可能通过排队等待服务而最终被服务，从而产生奖励。因此，接受作业的门槛降低，即最优阈值μ*减小。多方案对比：1) N从0增至较小的正整数（如N=1），μ*显著减小；2) N增至较大值（... | [
"在N=0的Erlang-B系统中，无排队，作业被接受后必须立即服务，系统饱和风险高，因此阈值μ*较高。",
"当N>0时，系统允许排队，这缓冲了到达波动，降低了饱和风险，使得在较低μ下接受作业也能获得奖励。",
"因此，N从0增至N>0，最优阈值μ*减小。",
"进一步，N越大，排队缓冲能力越强，阈值μ*越小。"
] | 2202.02419 | mimo | environment | null | null | needs_review | {
"arxiv_id": "2202.02419",
"title": "Learning to Admit Optimally in an MMkkN Queueing System with",
"authors": [],
"year": null,
"paper_path": "2202.02419_Learning_to_Admit_Optimally_in_an_MMkkN_Queueing_System_with",
"text_offset": 0
} | 考察对排队系统环境参数（队列容量N）变化下，最优控制策略（阈值μ*）敏感性的分析能力，要求基于模型机理进行多方案对比并给出明确工程结论。 | [
"未明确给出基准条件（N=0）和变化条件（N>0）的对比。",
"多方案对比不充分，仅分析单一变化方向（增大N），未考虑不同N值下的具体影响趋势。",
"工程结论不明确或未给出敏感性判定。",
"数学表达式或模型机理引用不准确。"
] | rejected | The paper does not discuss the effect of increasing N on the optimal threshold μ*. It only states that when N=0, the optimal policy is a threshold policy on μ (Section 1: 'if the service rate exceeds a value μ*, all arrivals are admitted... otherwise, all arrivals are rejected'). For N>0, the paper mentions that the di... | 0.95 | passed | rejected | 0.9 | 0.9 | The paper discusses the M/M/k/k+N system and mentions that when N=0, the optimal policy is a threshold on μ. The answer's reasoning that increasing N reduces the threshold is consistent with queueing theory intuition, though the paper does not explicitly analyze this sensitivity. The answer does not contradict any stat... | The paper states: 'When the waiting room N=0, then the optimal admission control algorithm which can use the system occupancy information only needs to choose between these two options; this is not true when N>0 where the dispatcher can use the system occupancy too.' This explicitly indicates that for N>0, the optimal ... | arxiv-only | [
"The paper does not analyze the sensitivity of μ* to N.",
"The answer's claim that μ* decreases with N is not based on any passage in the paper.",
"The paper focuses on learning μ, not on comparing μ* across different N."
] | [
"Major: The answer incorrectly assumes the optimal policy for N>0 remains a simple threshold policy based on μ*, contradicting the paper's statement that for N>0 the dispatcher can use system occupancy information, implying a more complex policy.",
"Major: The paper does not provide any analysis or claim about ho... | null | rejected | 0.95 | The paper explicitly states in the Introduction: 'When the waiting room N = 0, then the optimal admission control algorithm which can use the system occupancy information only needs to choose between these two options [always admit or never admit]; this is not true when N > 0 where the dispatcher can use the system occ... | [
"Major: The answer assumes the optimal policy for N>0 is a simple threshold on $μ$ (admit all vs block all), whereas the paper states the optimal policy for N>0 utilizes system occupancy information (state-dependent), making the premise of a single $μ^*$ threshold for the entire policy invalid.",
"Major: The sens... | null |
CS-EVO-00090 | D | L4 | [
"nonlinear",
"adaptive",
"robust"
] | 针对一类具有非严格全状态约束的未知非线性系统，设计一个自适应固定时间事件触发控制方案，使系统输出在固定时间内跟踪给定参考信号，同时保证所有状态不违反约束。请给出完整的控制方案设计，包括系统建模、控制器设计、事件触发机制设计以及性能验证指标。 | 1. 系统建模：考虑非严格全状态约束非线性系统 ẋ₁ = x₂, ẋᵢ = fᵢ(x̄ᵢ) + gᵢ(x̄ᵢ)uᵢ, i=2,...,n, y=x₁, 其中 x=[x₁,...,xₙ]ᵀ∈ℝⁿ, u∈ℝ。状态约束为 k_{b,i}(t) < xᵢ(t) < k_{a,i}(t)，k_{b,i}, k_{a,i}为已知光滑函数。参考信号为 y_d(t)。
2. 控制器选型：采用自适应固定时间控制结合径向基函数神经网络(RBFNN)逼近未知函数 fᵢ, gᵢ。控制目标是半全局实际固定时间稳定性(SPFTS)。
3. 参数整定：首先通过对数变换将约束系统转化为无约束纯反馈形式：zᵢ = ln((xᵢ - k_{b,i})/(k_{a,i}... | [
"识别被控对象为具有非严格全状态约束和未知非线性的严格反馈系统。",
"采用对数映射将约束系统转化为等效无约束系统以简化控制器设计。",
"选择自适应固定时间控制以实现与初始条件无关的收敛时间和鲁棒性。",
"集成RBFNN用于在线逼近未知非线性函数并设计自适应律更新其权重。",
"设计多阈值事件触发机制以降低通信频率，并包含预测项以实现自触发。",
"通过Lyapunov分析证明闭环系统的SPFTS性能并给出收敛时间上界。",
"在工程实现中考虑初始状态约束满足、神经网络初始化和触发参数整定。"
] | 2505.20870 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否在理论上可行，技术路线是否合理。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制方法的选择是否恰当且理由充分，是否结合了问题特点。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "回答是否覆盖了建模、控制器设计、触发机制... | needs_review | {
"arxiv_id": "2505.20870",
"title": "Effective Fixed Time Control for Constrained Nonlinear Syste",
"authors": [],
"year": null,
"paper_path": "2505.20870_Effective_Fixed_Time_Control_for_Constrained_Nonlinear_Syste",
"text_offset": 0
} | 本题考察设计完整自适应固定时间事件触发控制方案的能力，要求涵盖从建模到工程考量的全流程，Judge满分标准为方案逻辑完整、参数有依据、性能分析清晰、工程可行性高。 | [
"系统建模部分未正确转化约束或遗漏状态方程。",
"控制器设计未体现固定时间特性或自适应律。",
"事件触发机制设计不完整或未说明预测原理。",
"性能验证未给出SPFTS的数学表述或收敛时间分析。",
"工程考量流于形式，未结合控制方案具体讨论约束和实现难点。"
] | passed | The paper does not provide explicit system equations, controller design formulas, or event-triggered mechanism details as claimed in the answer. The abstract mentions 'adaptive fixed-time control method, utilizing a one-to-one asymmetric nonlinear mapping auxiliary system' and 'multi-threshold event-triggered control s... | 0.9 | passed | passed | 0.85 | 0.8 | The paper discusses adaptive fixed-time control for non-strict full-state constrained nonlinear systems, using nonlinear mapping (logarithmic transformation) to convert constrained systems into pure-feedback form, RBFNNs for approximation, event-triggered control strategies, and SPFTS stability. The answer's system mod... | The paper's abstract and introduction describe the core elements: 'adaptive fixed-time control method, utilizing a one-to-one asymmetric nonlinear mapping auxiliary system' (logarithmic transformation), 'multi-threshold event-triggered control strategies', and 'semi-global practical fixed-time stability (SPFTS)'. The a... | arxiv-only | [
"The system model equations (ẋ₁ = x₂, etc.) are not in the paper.",
"The specific virtual control law and adaptive law formulas are not provided in the paper.",
"The event-triggered function e(t)=‖s(t)‖-σ‖s(t-τ)‖-η e^{-λt} is not mentioned.",
"The paper does not specify the use of RBFNN for approximation in t... | [
"The answer's specific formulas (e.g., virtual control law αᵢ, trigger function e(t)) are plausible domain knowledge but are not explicitly detailed in the provided excerpt. This is acceptable as creative synthesis for a design question.",
"The answer mentions 'self-triggered' in the engineering considerations, w... | null | null | null | null | null | [
"The answer includes specific formulas (e.g., virtual control law with p_i, q_i, event-triggered function) that are not directly from the paper excerpt; however, they are reasonable extensions of the paper's concepts."
] |
CS-EVO-00091 | A | L1 | [
"classical"
] | 根据教材内容，第i个跟随者的动力学方程中，状态向量 $x_i$ 的最后一个状态分量 $\dot{x}_i^n$ 的表达式是什么？ | $\dot{x}_i^n = f_i(x_i) + u_i + w_i$。其中，$x_i = [x_i^1, x_i^2, \dots, x_i^n] \in \mathbb{R}^n$ 是第i个跟随者的状态向量，$f_i(x_i)$ 是一个局部Lipschitz且满足 $f_i(0)=0$ 的未知函数，$u_i \in \mathbb{R}$ 是第i个跟随者的控制输入，$w_i \in \mathbb{R}$ 是影响该跟随者的有界未知时变扰动。 | [
"定位到教材的 II. PROBLEM FORMULATION 部分，找到关于跟随者动力学方程的描述。",
"识别出方程 (1) 给出了状态导数的通用形式，其中最后一行明确给出了 $\\dot{x}_i^n$ 的表达式。",
"提取表达式 $\\dot{x}_i^n = f_i(x_i) + u_i + w_i$ 及其后对各项符号的说明。"
] | 2410.08440 | mimo | null | null | null | needs_review | {
"arxiv_id": "2410.08440",
"title": "Distributed Adaptive Consensus with Obstacle and Collision A",
"authors": [],
"year": null,
"paper_path": "2410.08440_Distributed_Adaptive_Consensus_with_Obstacle_and_Collision_A",
"text_offset": 0
} | 该题考察对多智能体系统基本动力学模型（Brunovsky标准形）数学表达式的精确回忆，要求能准确写出指定状态分量的导数表达式并说明各符号含义。 | [
"表达式写错或遗漏任何一项（如遗漏 $w_i$）。",
"未说明表达式中关键符号（如 $x_i$, $f_i$, $u_i$, $w_i$）的含义。",
"将 $f_i(x_i)$ 误写为 $f_i$ 或其它形式。"
] | passed | Section II, equation (1): '\dot{x}_i^n = f_i(x_i) + u_i + w_i' and the subsequent description: 'The unknown functions f_i(x) : R^n → R are locally Lipschitz in x with f_i(0)=0, for all i ∈ N.' | 1 | passed | passed | 1 | 1 | Section II, equation (1) states: '\dot{x}_i^n = f_i(x_i) + u_i + w_i'. The answer correctly reproduces this expression and explains the terms. | Section II, Equation (1) states: 'dot {x} _ {i} ^ {n} = f _ {i} (x _ {i}) + u _ {i} + w _ {i}'. The answer directly quotes this expression and correctly defines the components as described in the surrounding text. | arxiv-only | null | [
"API error: Error code: 429 - {'error': {'code': '429', 'message': 'Too many requests', 'type': 'limitation'}}"
] | null | null | null | null | null | null |
CS-EVO-00093 | B | L2 | [
"mpc"
] | 考虑一个简单的谐波模型预测控制（HMPC）系统，其人工谐波参考信号的形式为 r(k) = A sin(ωk + φ)，其中 A、ω、φ 为参数。若在某个时刻k0，优化问题求解得到的人工参考参数为 Â = 2 rad/s, ω̂ = 0.1π rad/s, φ̂ = 0，并已知系统的闭环状态 x(k0) = [1; 0]。请推导在k0+1时刻，HMPC控制器计算得到的人工参考信号值 r(k0+1)。 | 人工参考信号在 k0+1 时刻的值为 r(k0+1) = 2 sin(0.1π (k0+1) + 0) = 2 sin(0.1π k0 + 0.1π)。由于给定的具体时间 k0 未知，无法计算出一个具体的数值，但表达式为 2 sin(0.1π k0 + 0.1π)。 | [
"第一步：识别人工谐波参考信号的数学表达式为 r(k) = A sin(ωk + φ)。",
"第二步：将优化求解得到的参数 Â = 2, ω̂ = 0.1π, φ̂ = 0 代入上述表达式。",
"第三步：将时间索引从 k 替换为 k0+1，得到 r(k0+1) = 2 sin(0.1π (k0+1) + 0)。",
"第四步：展开表达式，得到 r(k0+1) = 2 sin(0.1π k0 + 0.1π)。"
] | 2310.16723 | mimo | null | null | null | needs_review | {
"arxiv_id": "2310.16723",
"title": "Harmonic model predictive control for tracking sinusoidal re",
"authors": [],
"year": null,
"paper_path": "2310.16723_Harmonic_model_predictive_control_for_tracking_sinusoidal_re",
"text_offset": 0
} | 本题考察对谐波模型预测控制中人工参考信号参数化形式的理解和基本代入计算能力。 | [
"未正确理解人工参考信号表达式中的参数含义。",
"在代入时间索引 k0+1 时出现计算错误。",
"未意识到由于 k0 未知，结果应为一个表达式而非具体数值。"
] | passed | The paper defines the harmonic artificial reference as a sinusoidal signal parameterized by amplitude, frequency, and phase. The answer correctly applies the formula r(k) = A sin(ωk + φ) with the given parameters to compute r(k0+1). | 1 | passed | passed | 0.95 | 0.9 | The paper defines the harmonic artificial reference as a parameterized sinusoidal signal (Section I: 'Harmonic signals (otherwise known as sinusoidal signals)'). The answer correctly applies the formula r(k) = A sin(ωk + φ) with the given parameters, noting that the exact numerical value depends on k0. This is consiste... | The paper states that HMPC uses a 'parameterized harmonic signal as an artificial reference' (Section I, paragraph 3) and that the proposed extension tracks 'harmonic/sinusoidal references' (Abstract). The answer correctly applies the given parameterization r(k) = A sin(ωk + φ) to compute r(k0+1) using the provided par... | arxiv-only | null | [
"Minor: The answer does not explicitly state that the artificial reference is a decision variable in the optimization problem, but this is not required for the calculation requested."
] | [
"B维答案缺少推导结论标记（未找到\"解得\"\"得到\"\"因此\"等结果标记）"
] | null | null | null | null | null |
CS-EVO-00094 | C | L2 | [
"optimal"
] | 在论文所描述的GLOSA随机最优控制问题中，假设基准条件下采用差分动态规划（DDP）算法进行求解。若将车辆到达交叉口时的速度约束范围从[0, 30] m/s增加到[0, 40] m/s，而其他所有参数（包括信号切换时间的随机分布、车辆动力学模型、燃油消耗模型等）保持不变，请分析该速度约束范围的扩大对DDP算法求解得到的最优速度策略的燃油消耗性能有何影响？ | 基准条件：速度约束为 v ∈ [0, 30] m/s。变化条件：速度约束放宽为 v ∈ [0, 40] m/s。对比分析：1. 约束放宽前，DDP算法在满足信号灯概率约束下，寻找燃油最优速度轨迹的可行解空间受限。2. 约束放宽后，可行解空间扩大，DDP算法可能找到燃油消耗更低的解（例如，允许更高速度以更少时间通过交叉口，避免停车）。数学上，设原问题为 min J(v) s.t. v ∈ [0, 30]，新问题为 min J(v) s.t. v ∈ [0, 40]。由于可行域扩大，最优值函数 J* 满足 J*_{new} ≤ J*_{old}。工程结论：速度约束范围的扩大对DDP算法的最优燃油消耗性能是敏感的，且变化方向明确——约束放... | [
"基准问题为在速度约束 v ∈ [0, 30] m/s 下，通过DDP算法求解随机GLOSA问题的燃油最优速度策略。",
"将速度约束条件放宽至 v ∈ [0, 40] m/s，保持其他所有参数和模型不变。",
"约束放宽导致可行域扩大，根据优化理论，扩大可行域不会使最优解变差。",
"因此，新问题的最优燃油消耗值 J*_{new} 必小于或等于原问题的最优值 J*_{old}。",
"结论是该参数变化（速度约束范围）对最优燃油性能有明确影响，且影响方向为性能提升或保持。"
] | 2211.12159 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2211.12159",
"title": "Modified Dynamic Programming Algorithms for GLOSA Systems wi",
"authors": [],
"year": null,
"paper_path": "2211.12159_Modified_Dynamic_Programming_Algorithms_for_GLOSA_Systems_wi",
"text_offset": 0
} | 考察对优化问题中约束条件变化对最优解性能影响的敏感性分析能力，要求基于优化理论进行多方案对比和明确结论。 | [
"未明确列出基准条件和变化条件的具体数值对比。",
"未能进行多方案对比（如未提及约束收紧的相反情况）。",
"工程结论不清晰或未给出明确的敏感性判定和建议。"
] | passed | The paper does not discuss the impact of changing speed constraints on DDP algorithm performance. It focuses on comparing DDP with SDP and DDDP in terms of computation time and solution quality under fixed problem settings. No analysis of varying speed bounds is provided. | 0.95 | passed | passed | 0.95 | 0.9 | The paper discusses DDP for stochastic GLOSA, and the answer's reasoning about feasible region expansion and potential fuel consumption improvement is consistent with optimal control theory. The paper does not explicitly discuss this scenario, but the answer does not contradict any part of the paper. | The paper states: 'It should be noted that DDP does not require discretization of variables, hence the obtained solutions may be slightly superior to the standard SDP solutions.' This implies that DDP can find solutions that are at least as good as those from SDP, and the answer's reasoning about a larger feasible set ... | redistributable | [
"The answer speculates about the effect of speed constraint changes without any support from the paper.",
"The paper does not contain any experiments or analysis regarding different speed constraint ranges.",
"The mathematical reasoning about feasible regions and optimal value functions is not derived from the ... | [
"The answer is a general optimization principle and does not directly contradict the paper, but the paper does not explicitly discuss the effect of changing the speed constraint range. The answer's conclusion is reasonable domain knowledge but not explicitly verified by the provided excerpt."
] | [
"C维只有单一方向分析（仅有\"升高\"方向，缺少多方向对比）"
] | null | null | null | null | null |
CS-EVO-00095 | D | L4 | [
"adaptive",
"nonlinear"
] | 针对论文中提出的稳定性保证双卡尔曼滤波（SG-DKF）方法，设计一个完整的控制方案用于电池荷电状态（SOC）估计。请明确给出该方案的系统建模、控制器选型、参数整定、性能验证指标和工程考量，并确保方案能应对大初始化误差。 | 1. 系统建模：采用简化电化学模型（单粒子模型，SPM）描述电池动力学。状态方程：dC_s/dt = (D_s/r_s^2) * ∂^2 C_s/∂x^2，其中C_s为固相锂离子浓度，D_s为扩散系数，r_s为粒子半径。测量方程：V_t = OCP(SOC) - I*t/C_n - R_int*I - η，其中V_t为端电压，OCP为开路电压，I为电流，C_n为额定容量，R_int为内阻，η为过电位。离散化后得非线性状态空间模型。
2. 控制器选型：采用稳定性保证双卡尔曼滤波（SG-DKF）。选择理由：SG-DKF通过Lyapunov分析引入自适应死区规则，当新息超过稳定性界限时暂停参数更新，能有效抑制因大初始化误差或模型失配导致的... | [
"SG-DKF方案需要建立电池的电化学模型，采用SPM作为简化模型以平衡精度与计算量。",
"SG-DKF是针对传统双卡尔曼滤波器耦合发散问题的改进方法，其Lyapunov稳定性分析和死区规则是核心。",
"参数整定需基于Lyapunov稳定性条件设定死区阈值，其他协方差矩阵根据经验或仿真调优。",
"性能验证需覆盖稳定性、准确性（RMSE）、快速性（收敛时间）等关键指标。",
"工程实施需考虑计算复杂度、噪声、老化等实际约束，确保方案可部署。"
] | 2512.04885 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案技术可行，数学模型和参数选择合理，能在电池系统上实施。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择SG-DKF有充分理由，紧扣论文内容和解决大初始化误差问题的需求。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "回答包... | needs_review | {
"arxiv_id": "2512.04885",
"title": "Stability Guaranteed Dual Kalman Filtering for Electrochemic",
"authors": [],
"year": 2018,
"paper_path": "2512.04885_Stability_Guaranteed_Dual_Kalman_Filtering_for_Electrochemic",
"text_offset": 0
} | 该题考察设计一个基于SG-DKF的电池SOC估计完整控制方案的能力，要求涵盖建模、选型、整定、验证和工程化五个方面，Judge满分标准为方案完整、参数具体、性能分析全面且工程考量合理。 | [
"方案不完整，缺少五个要求部分中的任意一项。",
"参数整定未给出具体数值或整定依据。",
"性能验证未包含关键指标（如稳定裕度、收敛时间）。",
"工程考量过于泛泛，未结合SG-DKF特点或电池应用约束。"
] | passed | The paper does not provide specific numerical values for parameter tuning (e.g., P_x0, P_θ0, Q_x, Q_θ, R, ε) or performance metrics like convergence time. The paper states: 'Applied to an electrochemical battery model, SG-DKF achieves accuracy comparable to a dual EKF and reduces state of charge RMSE by over 45% under ... | 0.95 | passed | passed | 0.9 | 0.9 | The paper proposes SG-DKF with Lyapunov-based stability analysis and adaptive dead-zone rule (Section 1, 3). The answer correctly uses SPM, SG-DKF, and mentions dead-zone rule. The 45% RMSE reduction is stated in the abstract. The answer's additional details (e.g., specific covariance values, convergence time) are reas... | The paper proposes SG-DKF for electrochemical battery models, specifically mentioning the single particle model (SPM) as a reduced-order model. The answer correctly identifies the core components: system modeling with SPM, controller selection as SG-DKF with its adaptive dead-zone rule, and performance metrics like RMS... | arxiv-only | [
"The answer invents specific numerical values for covariance matrices and dead-zone threshold not present in the paper.",
"The answer provides a detailed system model (SPM equations) not explicitly given in the paper.",
"The answer lists performance metrics (e.g., convergence time <10s) not mentioned in the pap... | [
"Minor: The answer provides specific numerical values for parameters (e.g., P_x0, Q_x, R, ε) that are not specified in the paper excerpt. This is acceptable as reasonable engineering estimates, but should be noted as illustrative rather than derived from the source.",
"Minor: The answer's state equation for SPM i... | null | null | null | null | null | [
"The paper does not specify exact numerical values for covariances or dead-zone threshold; these are plausible but not from the paper."
] |
CS-EVO-00096 | A | L2 | [
"robust"
] | 在鲁棒预设时间协调控制的研究中，针对无干扰的标称单积分器合作-对抗网络，所提出的全分布式控制协议具有什么核心特征？ | 该控制协议是一个具有时变增益的全分布式协议。其核心特征在于，该时变增益会随着趋近设定时间（settling time）而趋于无穷大。该协议仅利用相邻智能体的相对状态信息进行设计。 | [
"在摘要和引言中，论文明确指出为标称单积分器合作-对抗网络（无干扰）提出了一个全分布式控制协议。",
"该协议的关键特征被描述为使用一个“时变增益”，并且这个增益“随着趋近设定时间而趋于无穷大”。",
"该协议的设计基础是“利用相邻智能体的相对状态”。"
] | 2210.11212 | mimo | null | null | null | needs_review | {
"arxiv_id": "2210.11212",
"title": "Robust prescribed time coordination control of cooperative a",
"authors": [],
"year": null,
"paper_path": "2210.11212_Robust_prescribed_time_coordination_control_of_cooperative_a",
"text_offset": 0
} | 该题考察对论文核心方法（预设时间控制协议）关键特征的准确记忆和理解，满分标准是能精确指出“时变增益在趋近设定时间时趋于无穷大”这一特征。 | [
"遗漏“全分布式”或“利用相对状态”等设计特点。",
"未能准确描述时变增益的行为（如只说“增益变化”而未指明趋于无穷大）。",
"将协议与存在干扰时使用的二阶滑模控制协议混淆。"
] | passed | Section I (Introduction) states: 'a fully distributed control protocol with a time-varying gain, which grows to infinity as the time approaches the settling time, is proposed utilizing the relative states of neighboring agents.' | 1 | passed | passed | 0.95 | 0.95 | The paper states: 'a fully distributed control protocol with a time-varying gain, which grows to infinity as the time approaches the settling time, is proposed utilizing the relative states of neighboring agents.' This matches the answer exactly. | The abstract states: 'a fully distributed control protocol with a time-varying gain, which grows to infinity as the time approaches the settling time, is proposed utilizing the relative states of neighboring agents.' This directly matches the answer's description of the protocol's core features. | redistributable | null | null | [
"A维答案过于模糊：缺少 LaTeX 公式、条件-结论结构、或 ≥3 个控制科学术语",
" - 未检测到 LaTeX 公式标记",
" - 未检测到条件-结论结构",
" - 控制科学术语不足（仅 1/3）"
] | null | null | null | null | null |
CS-EVO-00097 | C | L4 | [
"adaptive",
"optimal"
] | 考虑论文中提出的离散时间事件触发极值搜索控制系统，其性能依赖于未知Hessian参数 H*。假设在基准条件下，系统能够保证轨迹收敛到未知极值点的一个邻域内。现在，保持其他所有条件不变，仅将H*的绝对值从基准值增大到原来的10倍，分析这种变化对系统收敛邻域大小的影响，并判断原结论（即实用收敛性）是否仍然保持？ | 基准条件复述：根据论文公式(1)，静态性能指标映射为 Q[θ[k]] = Q* + (H*/2)(θ[k] - θ*)²，其中 H* ≠ 0 是未知Hessian参数。原分析（离散时间平均与Lyapunov方法）表明，在基准 H* 下，闭环轨迹会收敛到未知极值点 Q* 的一个邻域内（实用收敛性）。
变化条件分析：将 H* 的绝对值 |H*| 从基准值 H₀ 增大到 10|H₀|。变化前，收敛邻域的大小与 |H*| 有关（具体大小依赖于论文中未给出的系统参数与触发条件细节）。变化后，|H*| 增大，导致性能函数在极值点附近更陡峭（曲率增大）。
多方案对比：1) 若 |H*| 增大（如增至10倍），性能函数对 θ 偏差更敏感，可能导致收... | [
"论文公式(1)定义了性能映射 Q[θ[k]] = Q* + (H*/2)(θ[k] - θ*)²，其中 H* 是未知Hessian参数。",
"论文的离散时间平均与Lyapunov分析证明了闭环轨迹实用收敛到极值点邻域，该证明不依赖于 H* 的具体数值（仅要求 H* ≠ 0）。",
"将 H* 的绝对值从 |H₀| 增大到 10|H₀|，性能函数在 θ* 附近的曲率增大为原来的10倍。",
"更大的曲率意味着极值搜索扰动信号会引发更大的性能波动，可能导致收敛邻域增大。",
"原实用收敛性结论保持，因为分析框架对 H* 的数值不敏感；但邻域大小对 |H*| 敏感。"
] | 2604.01450 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2604.01450",
"title": "Discrete Time Event Triggered Extremum Seeking",
"authors": [],
"year": null,
"paper_path": "2604.01450_Discrete_Time_Event_Triggered_Extremum_Seeking",
"text_offset": 0
} | 该题考察对事件触发极值搜索系统中关键未知参数（Hessian）变化时，系统收敛性结论的鲁棒性分析，以及多方案对比下的敏感性评估。 | [
"可能未完整复述基准条件（公式(1)和收敛性结论）",
"可能未量化变化前后的差异（如未提及曲率变化10倍）",
"可能缺少多方案对比（如只分析了增大情况，未提及减小情况）",
"工程结论可能不够明确（如未指出实用收敛性保持但邻域可能变化）"
] | passed | The paper does not provide any analysis or discussion on how the magnitude of H* affects the size of the convergence neighborhood. The answer speculates about the effect without support from the paper. The paper only states that H* is unknown and nonzero, and that practical convergence is established, but does not rela... | 0.9 | passed | passed | 0.85 | 0.9 | The paper's analysis framework (discrete-time averaging and Lyapunov) does not impose specific bounds on H* beyond H* ≠ 0. The answer correctly notes that practical convergence holds for any H* ≠ 0, and that the convergence neighborhood size depends on |H*|, which is consistent with the quadratic map (1). The answer's ... | The paper states in the Abstract and Introduction that the method establishes 'practical convergence of the trajectories to a neighborhood of the unknown extremum point'. The problem formulation defines Q[θ[k]] = Q* + (H*/2)(θ[k] - θ*)² with H* ≠ 0. The answer correctly identifies that the convergence is to a neighborh... | redistributable | [
"The answer claims that increasing |H*| leads to a larger convergence neighborhood, but this is not supported by the paper.",
"The answer suggests that the practical convergence conclusion remains valid for any H* ≠ 0, which is not explicitly stated in the paper; the analysis may rely on specific assumptions abou... | [
"The answer's speculation about the specific relationship between |H*| and the neighborhood size (e.g., 'larger |H*| leads to larger neighborhood') is not explicitly derived or stated in the provided paper excerpt. While this is a reasonable engineering inference based on the quadratic form, the paper's analysis de... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | [
"The answer speculates about the effect of |H*| on convergence neighborhood size without direct support from the paper excerpt; however, this is reasonable domain knowledge and does not contradict the paper."
] |
CS-EVO-00098 | D | L4 | [
"digital",
"robust"
] | 针对文中描述的差速驱动机器人网络化控制系统，其内部模型（EMC单元）的稳定性依赖于观测器增益矩阵L的设计。请设计一个完整的EMC控制方案，以确保该内部模型在异步控制时序下保持渐近稳定。具体工程约束为：闭环系统所有极点应位于z平面半径为0.9的单位圆内，且控制器必须能处理文中提到的测量延迟和异步执行问题。 | 1. 系统建模：采用文中公式(1)的离散状态空间模型：x(k+1) = A x(k) + B u(k) + G w(k)，y_m(k) = C x(k)。其中A为分块矩阵，包含可控子矩阵A_c、抑制器子矩阵A_d及交互项H_c。
2. 控制器选型：选择嵌入式模型控制（EMC）方案。理由：EMC通过内部模型和观测器结构能显式处理异步时序和测量延迟，适合网络化控制场景。
3. 参数整定：设计观测器增益矩阵L。首先，确定闭环特征多项式 det(zI - (A - G L C)) = ∏(z - p_i)，其中所有极点p_i需满足|p_i| < 0.9。可通过极点配置法求解L，例如采用Ackermann公式，使极点位于z=0.85附近。
4... | [
"题目要求设计EMC控制方案以确保内部模型在异步时序下稳定，并给定极点约束。",
"建模需引用文中公式(1)的状态空间形式，这是EMC的基础。",
"控制器选型必须基于EMC，因其专门处理网络化控制中的异步问题，这是论文核心。",
"参数整定需针对观测器增益L，并依据给定的极点半径约束（0.9）进行设计，这是稳定性的关键。",
"性能验证需覆盖内部模型稳定性（极点位置）和BIBO稳定性，并关联到工程约束。",
"工程考量必须讨论异步时序的实际实施挑战，如计算延迟和缓冲。"
] | 2211.08080 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案基于论文EMC框架，数学模型正确，工程约束合理。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择EMC并给出充分理由，与网络化控制异步问题匹配。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "包含建模、选型、整定、验证、工... | needs_review | {
"arxiv_id": "2211.08080",
"title": "Embedded Model Control of Networked Control Systems an Exper",
"authors": [],
"year": null,
"paper_path": "2211.08080_Embedded_Model_Control_of_Networked_Control_Systems_an_Exper",
"text_offset": 0
} | 该题考察被测试者根据论文内容设计EMC控制方案的能力，包括从模型建立、控制器选择、参数整定到性能分析和工程实施的完整设计思维，满分标准为方案完整、参数有据、分析全面、考虑工程实际。 | [
"可能扣分点：未完整建立或引用文中模型(1)。",
"可能扣分点：控制器选型理由未紧扣EMC处理异步时序的优势。",
"可能扣分点：参数整定过程未明确如何满足极点约束。",
"可能扣分点：工程考量未提及网络化系统中的具体约束（如延迟、丢包）。"
] | passed | The paper does not provide a complete EMC control scheme design; it only discusses stability analysis and mentions that stability depends on observer gain L design (Section 2.1). The answer invents specific pole locations (0.85) and design methods (Ackermann) not present in the paper. The paper does not give a step-by-... | 0.9 | passed | passed | 0.9 | 0.9 | The paper discusses stability analysis of the EMC internal model, stating that stability depends on the observer matrix L design (Section 2.1). The answer correctly references the state-space model (1) and the characteristic polynomial det(zI - (A - G L C)) for pole placement. The requirement for poles inside the unit ... | Section 2.1 states: 'Both the internal and BIBO stability of the internal model can be studied by imposing det{zI − [A − G L C]} equal to a characteristic polynomial... in order to guarantee the asymptotic stability, the poles [p1, p2, ..., pn] must lie inside the unitary circle. From the equation above it is clear tha... | redistributable | [
"Answer invents specific pole location (0.85) not mentioned in paper.",
"Answer invents design method (Ackermann formula) not mentioned in paper.",
"Answer provides a complete design scheme not present in the paper.",
"Paper only discusses stability analysis, not controller design steps."
] | [
"Minor: The answer's specific pole location (z=0.85) is a reasonable engineering choice but not specified in the paper. This is acceptable as a design example.",
"Minor: The answer mentions 'Ackermann formula' and 'buffer mechanism', which are standard control engineering techniques not explicitly detailed in the... | null | null | null | null | null | null |
CS-EVO-00099 | B | L4 | [
"classical",
"modern"
] | 考虑一个离散时间LTI系统，其广义被控对象（1）中的系统矩阵为：A = [1, 2; 0, 1], B_w = [0; 1], B_u = [0; 1], C_z = [1, 0], D_zw = 0, D_zu = 0, C_y = [0, 1], D_yw = 0。假设设计一个静态状态反馈控制器 u(t) = K x(t)，其中 K 是 1×2 的增益矩阵。请推导该闭环系统在扰动 w(t) 作用下，性能输出 z(t) 的稳态方差 Var(z) = lim_{T→∞} (1/T) ∑_{t=0}^{T-1} E[||z(t)||^2] 关于增益 K 的表达式。 | 闭环系统状态方程为 x(t+1) = (A + B_u K) x(t) + B_w w(t)。性能输出为 z(t) = C_z x(t)。假设 w(t) 为零均值白噪声，其方差为 Q_w = E[w(t)w(t)^T] = σ^2。定义闭环系统矩阵 A_cl = A + B_u K。则稳态状态协方差矩阵 P = lim_{t→∞} E[x(t)x(t)^T] 满足离散Lyapunov方程 A_cl P A_cl^T - P + B_w Q_w B_w^T = 0。性能输出稳态方差为 Var(z) = C_z P C_z^T。将具体矩阵代入：A = [[1, 2], [0, 1]], B_u = [0; 1], C_z = [1, 0... | [
"将静态状态反馈 u = Kx 代入被控对象（1）的闭环系统，得到闭环状态方程 x(t+1) = (A + B_u K) x(t) + B_w w(t) 和性能输出方程 z(t) = C_z x(t)。",
"根据性能输出方差定义，Var(z) = lim_{T→∞} (1/T) ∑_{t=0}^{T-1} E[||z(t)||^2] = lim_{t→∞} E[z(t)z(t)^T] = C_z P C_z^T，其中 P 是闭环系统的稳态状态协方差矩阵。",
"协方差矩阵 P 满足离散Lyapunov方程 A_cl P A_cl^T - P + B_w Q_w B_w^T = 0，其中 A_cl = A + B_u... | 2509.23493 | mimo | null | null | null | needs_review | {
"arxiv_id": "2509.23493",
"title": "Distributionally robust LMI synthesis for LTI systems",
"authors": [],
"year": null,
"paper_path": "2509.23493_Distributionally_robust_LMI_synthesis_for_LTI_systems",
"text_offset": 0
} | 该题考察从系统状态空间描述出发，结合状态反馈控制和随机过程统计特性，通过多步推导得出性能指标表达式的能力。 | [
"未能正确写出闭环状态方程 A_cl。",
"错误推导或漏写离散Lyapunov方程。",
"代数求解 P 或最终表达式时出现计算错误。",
"未提及保证闭环系统稳定的条件（如 |1 + k2| < 1）。"
] | rejected | The paper does not provide any specific numerical example or derivation for a static state feedback controller with given matrices. The answer's derivation and final expression are not supported by the paper. | 1 | rejected | rejected | 0.95 | 0.9 | The paper considers output-feedback dynamic controllers (2) and a cost function (4) that involves a supremum over disturbance distributions in an ambiguity set W. The answer assumes a static state feedback controller and a specific white noise disturbance model, which are not discussed in the paper. The paper's problem... | The paper defines the cost function in (4a) as v(A_c, B_c, C_c, D_c) = sup_{w∈W} limsup_{T→∞} (1/T) ∑_{t=0}^{T-1} E[||z(t)||^2]. The answer incorrectly assumes w(t) is a zero-mean white noise with variance σ^2 and computes a steady-state variance. However, the paper's formulation is a distributionally robust problem wh... | arxiv-only | [
"The paper does not contain the specific system matrices or the derivation of the steady-state variance expression.",
"The answer assumes a static state feedback controller, while the paper focuses on dynamic output feedback controllers.",
"The Lyapunov equation and variance expression are standard results, but... | [
"The answer incorrectly treats the problem as a standard stochastic control problem with a specific noise model, ignoring the distributionally robust formulation (supremum over ambiguity set W) defined in the paper.",
"The answer's final expression for Var(z) appears to be a specific algebraic result for a partic... | [
"B维答案缺少推导结论标记（未找到\"解得\"\"得到\"\"因此\"等结果标记）"
] | null | null | null | null | [
"The answer assumes static state feedback, while the paper considers dynamic output feedback.",
"The answer assumes a specific white noise disturbance with known variance, while the paper considers distributionally robust disturbances.",
"The derived expression for Var(z) is not supported by the paper and may c... |
CS-EVO-00100 | C | L3 | [
"classical"
] | 在论文所分析的多智能体模型预测博弈控制系统中，若所有智能体的博弈模型参数（例如其二次型代价函数中的权重矩阵Q和R）发生相同的、一致的缩放变化（例如同时乘以一个大于1的正常数α），那么该缩放变化对系统平衡点的预测敏感性有何影响？ | 基准条件：系统由N个异构智能体组成，每个智能体i在其控制周期内求解一个有限时域开环博弈问题，其目标函数为 J_i(u) = Σ_{k=0}^{N_p-1} [x_k^T Q_i x_k + u_{i,k}^T R_i u_{i,k}] + x_{N_p}^T P_i x_{N_p}。变化条件：将所有智能体的代价函数权重矩阵同时缩放为 αQ_i 和 αR_i，其中 α > 1 为正常数。多方案对比：1. α增大（如α=2）：平衡点预测对系统状态和控制量的相对惩罚保持不变，因为目标函数整体缩放不影响优化问题的最优解（即纳什均衡控制序列{u_{i,k}}*不变），因此预测敏感性不变。2. α减小（如α=0.5）：同理，只要α为正常数，最优... | [
"在基准条件下，每个智能体i的控制问题为求解一个以加权二次型和为目标的有限时域博弈，其纳什均衡解由权重矩阵Q_i, R_i, P_i决定。",
"将参数缩放为αQ_i和αR_i后，每个智能体的目标函数变为原目标函数的α倍。",
"由于优化问题的目标函数仅乘以一个正常数因子，其最优解集（即纳什均衡控制序列）与原问题完全相同。",
"因此，缩放前后的平衡点预测值完全一致，预测对参数变化的敏感性为零。",
"对于α增大或减小（α>0）的两种情况，上述推理均成立，结论一致。"
] | 2604.08303 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2604.08303",
"title": "Stability and Sensitivity Analysis for Objective Misspecific",
"authors": [],
"year": null,
"paper_path": "2604.08303_Stability_and_Sensitivity_Analysis_for_Objective_Misspecific",
"text_offset": 0
} | 本题考察对模型预测博弈控制器参数敏感性分析的理解，要求能区分参数的等价变换与实质性变化，并做出准确的敏感性判定。 | [
"未明确指出等比例缩放不影响优化问题最优解这一核心机制。",
"未进行多方案对比（如仅分析α>1或未分析α<1的情况）。",
"工程结论未能明确指出敏感性不变或敏感性为零。",
"数学表达不完整或推导逻辑不清晰。"
] | passed | The paper does not discuss the effect of scaling all agents' cost function weights uniformly. It focuses on misspecifications where agents have different models, not identical scaling. The answer's claim that scaling does not affect the Nash equilibrium is a general property of LQ games, but the paper does not address ... | 1 | passed | rejected | 0.95 | 0.9 | The paper discusses sensitivity of equilibria to individual agents' game parameters (Section I: 'quantify the sensitivity of the equilibria to individual agents’ game parameters'). The answer's reasoning that scaling all cost weights by the same positive constant does not change the Nash equilibrium is a standard prope... | The paper's abstract and introduction focus on misspecifications in agents' *objectives* (i.e., different agents having different, potentially incorrect, models of each other's goals). The paper analyzes the sensitivity of equilibria to *heterogeneous* game parameters. The answer incorrectly assumes that scaling all ag... | redistributable | [
"The paper does not analyze uniform scaling of all agents' cost weights.",
"The answer assumes a property of LQ games without citing the paper.",
"The paper's sensitivity analysis is about heterogeneous misspecifications, not identical scaling."
] | [
"Major factual error: The claim that scaling all agents' cost functions by the same α leaves the Nash equilibrium unchanged is incorrect. In a non-cooperative game, scaling all players' payoff functions by the same positive constant does not preserve the Nash equilibrium in general, as it changes the relative impor... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | passed | 0.95 | Auditor B's rejection is based on a fundamental misunderstanding of Nash Equilibrium properties in non-cooperative games. In a standard non-cooperative game (which is the context of Model Predictive Games as described in the Introduction: 'interactions... approximated as noncooperative dynamic games'), each agent minim... | [
"Auditor B made a major factual error regarding Game Theory fundamentals: claiming that uniform positive scaling of all players' cost functions changes the Nash Equilibrium in a non-cooperative game."
] | null |
CS-EVO-00101 | D | L3 | [
"adaptive",
"intelligent"
] | 为一架在动态风扰动下进行轨迹跟踪的四旋翼无人机，设计一个基于全深度神经网络（DNN）的自适应控制方案。请给出：1）系统动力学模型；2）控制律与自适应律的具体形式；3）关键性能指标（如稳定裕度、响应时间、稳态误差）的分析方法；4）实际工程实施中需要考虑的约束与注意事项。 | 1. 系统建模：考虑四旋翼动力学，其姿态子系统可表示为 $I\ddot{\theta} = \tau + \Delta(t, \theta, \dot{\theta})$，其中 $I$ 为转动惯量矩阵，$\tau$ 为控制力矩，$\Delta$ 为未知扰动（包括风扰）。2. 控制器选型与参数整定：采用本文提出的SSML-AC框架。离线阶段通过自监督元学习（SSML）预训练DNN $f_{\phi}(x)$，使其基于历史状态 $x$ 预测未来扰动 $\Delta$。在线阶段，控制律设计为 $\tau = \tau_{ff} - K \dot{e} - \hat{\Delta}$，其中 $\tau_{ff}$ 为前馈力矩，$K$ 为正定... | [
"第一步：根据四旋翼动力学建立包含未知扰动的运动学方程。",
"第二步：基于论文提出的SSML-AC框架，确定离线自监督预训练与在线复合自适应的两阶段策略，并写出控制律和自适应律的数学形式。",
"第三步：利用李雅普诺夫稳定性分析为参数整定提供理论依据，具体构造函数并推导稳定条件。",
"第四步：明确性能验证需结合理论分析（稳定性）与实验指标（时域、频域），并指出关键指标。",
"第五步：讨论实际工程约束，如计算、实时性、噪声和安全。"
] | 2410.07575 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在理论和工程上是否可行，是否符合四旋翼控制的基本要求。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "是否选择了与论文内容一致的SSML-AC框架，并说明了选择理由。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否完整覆盖... | needs_review | {
"arxiv_id": "2410.07575",
"title": "Self Supervised Meta Learning for All Layer DNN Based Adapti",
"authors": [],
"year": null,
"paper_path": "2410.07575_Self_Supervised_Meta_Learning_for_All_Layer_DNN_Based_Adapti",
"text_offset": 0
} | 该题考察设计完整学习型自适应控制方案的能力，要求涵盖建模、控制器设计、参数整定、性能验证和工程考量五个完整环节，Judge满分标准为方案完整、参数有理论依据、性能分析清晰、工程考量全面。 | [
"系统建模不完整或未考虑扰动项。",
"控制律/自适应律形式错误或未与SSML-AC框架对齐。",
"参数整定过程缺乏稳定性分析的支撑。",
"性能验证仅列出指标而未说明分析方法。",
"工程考量过于笼统，未结合DNN自适应控制特点。"
] | passed | The paper does not provide a specific system dynamics model like $I\ddot{\theta} = \tau + \Delta(t, \theta, \dot{\theta})$. The control law in the paper is not given as $\tau = \tau_{ff} - K \dot{e} - \hat{\Delta}$; instead, the paper describes a control law and adaptation law in general terms without explicit equation... | 0.95 | passed | passed | 0.9 | 0.9 | The answer correctly describes the SSML-AC framework from the paper: offline self-supervised meta-learning pretraining and online full DNN adaptation with composite adaptation. The control law and adaptation law are consistent with the paper's description (speed-gradient composite adaptation). The Lyapunov analysis and... | The paper's abstract and introduction describe the SSML-AC framework: 'pretrains a DNN via self-supervised meta-learning (SSML) from offline trajectories and online adapts the full DNN via composite adaptation.' The answer correctly identifies the core components: offline SSML pretraining of a DNN to predict disturbanc... | arxiv-only | [
"The system dynamics model is not provided in the paper.",
"The control law and adaptation law equations are not given in the paper.",
"The Lyapunov function and stability analysis details are not in the paper.",
"Performance metrics analysis methods are not discussed.",
"Engineering constraints are not ela... | [
"Minor: The answer's specific control law form (τ = τ_ff - K ė - Δ̂) and adaptation law (θ̇ = -Γ e_f ∇_θ f_θ(x)) are plausible engineering instantiations but are not explicitly detailed in the provided excerpt. The paper mentions a 'speed-gradient composite adaptation law' but does not give the exact equation. This... | null | null | null | null | null | null |
CS-EVO-00102 | B | L3 | [
"classical",
"modern"
] | 考虑论文中描述的带彩色噪声的线性系统，其状态空间模型如式(1)所示。若过程噪声 w 和测量噪声 z 均通过将白噪声与宽度为 s 的高斯滤波器卷积生成，且该高斯滤波器的冲激响应为 h(t) = (1/√(2π)s) exp(-t²/(2s²))。试推导将彩色噪声表示为白噪声激励一个动态系统时的等价状态空间描述。 | 将彩色噪声 w_c(t) 视为白噪声 w_w(t) 通过线性时不变滤波器 h(t) 生成。由于 h(t) 是高斯函数，其对应的传递函数为 H(s) = exp(-s²s²/2)，这不是一个有限维线性系统，因此无法用一个有限维的状态空间微分方程来精确表示。一种常用的近似方法是将高斯滤波器用一个一阶或二阶的低通滤波器（如 h(t) ≈ (1/τ)exp(-t/τ)）来拟合，从而得到等价的动态系统。例如，采用一阶近似时，等价的噪声动态为 ṡ = -s/τ + w_w(t)，此时噪声平滑度参数 s 对应于滤波器的时间常数 τ。 | [
"第一步：识别彩色噪声是由白噪声通过高斯滤波器卷积生成，其冲激响应 h(t) 为高斯函数。",
"第二步：判断高斯函数的拉普拉斯变换不是有理分式，因此不能精确表示为一个有限维的线性微分方程组（即状态空间模型）。",
"第三步：根据控制理论中处理有色噪声的常规方法（如状态增广），提出用一个可实现的近似动态系统（如一阶系统）来代替高斯滤波器，并给出近似后的等价状态空间描述形式。"
] | 2204.01796 | mimo | null | null | null | needs_review | {
"arxiv_id": "2204.01796",
"title": "Free Energy Principle for the Noise Smoothness Estimation of",
"authors": [],
"year": null,
"paper_path": "2204.01796_Free_Energy_Principle_for_the_Noise_Smoothness_Estimation_of",
"text_offset": 0
} | 本题考察对论文中彩色噪声生成模型（高斯滤波）的数学理解，并将其转化为控制理论中常用的状态空间描述的推导能力，需要结合信号处理和状态空间建模的多步推理。 | [
"未能指出高斯滤波器对应的系统是无限维的，不能精确用有限维状态空间表示。",
"在给出近似方法时，未正确建立近似滤波器的状态空间方程（例如一阶系统的状态方程）。",
"推导过程跳跃，未清晰展示从卷积关系到微分方程或状态空间模型的逻辑步骤。",
"混淆了噪声平滑度参数 s 与滤波器时间常数的对应关系。"
] | rejected | The paper states: 'The noises in this paper are generated through the convolution of white noise with a Gaussian filter of kernel width s.' It does not provide any derivation or approximation of the colored noise as a dynamic system. The answer's claim about the transfer function H(s)=exp(-s²s²/2) and the approximation... | 1 | passed | rejected | 0.9 | 0.9 | The paper states that noises are generated through convolution of white noise with a Gaussian filter of kernel width s (Section III). The answer correctly identifies that the Gaussian filter leads to an infinite-dimensional system and suggests a finite-dimensional approximation, which is a reasonable engineering approa... | Section III states: 'The noises in this paper are generated through the convolution of white noise with a Gaussian filter of kernel width s.' The paper does not provide the specific Gaussian impulse response formula h(t) = (1/√(2π)s) exp(-t²/(2s²)) as stated in the question. More critically, the answer incorrectly clai... | arxiv-only | [
"The answer introduces a transfer function and approximation not mentioned in the paper.",
"The paper does not discuss representing colored noise via a dynamic system; it only states the generation method.",
"The answer's derivation is not supported by the source paper."
] | [
"The answer incorrectly states that the Gaussian filter cannot be represented by a finite-dimensional state-space model, which contradicts the paper's fundamental approach of designing a state-space observer (DEMs) for this exact scenario.",
"The answer introduces an approximation (first-order low-pass filter) th... | null | rejected | 0.95 | Auditor B is correct. The paper's core contribution is the 'DEMs' (Dynamic Expectation Maximization) observer, which relies on the 'Generalized Filtering' framework from neuroscience. In this framework, colored noise generated by a Gaussian filter is handled not by approximating the filter with a finite-dimensional ODE... | [
"The answer claims Gaussian noise cannot be represented by a finite-dimensional state-space model, ignoring the paper's use of Generalized Coordinates (DEMs) which handles this exact case.",
"The answer proposes a first-order approximation which is not part of the paper's method and is less accurate than the DEMs... | null |
CS-EVO-00103 | A | L1 | [
"classical"
] | 在本文提出的基于深度神经网络的滑模控制策略中，用于证明系统稳定性的李雅普诺夫函数（Lyapunov function）设计所依据的核心判据是什么？ | 核心判据是：如果一个标量函数V(x)正定（V(x)>0，当x≠0时；V(0)=0），且其时间导数dV/dt沿系统轨迹负定（dV/dt<0，当x≠0时；dV/dt(0)=0），则该系统的平衡点是渐近稳定的。此判据确保了系统状态能从任意初始点收敛至平衡点。 | [
"第一步：确定文中用于稳定性证明的工具是李雅普诺夫函数。",
"第二步：李雅普诺夫稳定性判据要求函数V(x)必须正定。",
"第三步：同时要求V(x)沿系统状态轨迹的时间导数必须负定。",
"第四步：结合这两个条件，构成渐近稳定的充分条件。"
] | 2405.15493 | mimo | null | null | null | needs_review | {
"arxiv_id": "2405.15493",
"title": "Design and Implementation of DC DC Buck Converter based on D",
"authors": [],
"year": null,
"paper_path": "2405.15493_Design_and_Implementation_of_DC_DC_Buck_Converter_based_on_D",
"text_offset": 0
} | 该题考察李雅普诺夫稳定性判据的精确表述，满分标准是完整、准确地陈述函数正定和导数负定这两个核心条件及其含义。 | [
"遗漏V(x)正定或dV/dt负定中的任一条件。",
"未说明“当x≠0时”或“V(0)=0”等具体状态条件。",
"未提及“渐近稳定”这一结论。"
] | passed | The paper states: 'To demonstrate the stability of the system, a Lyapunov function is designed to prove the stability of the mathematical model of the DNN-based sliding mode control strategy for DC-DC buck switching power supply.' However, the paper does not provide the specific Lyapunov function or its derivative cond... | 0.9 | passed | passed | 0.95 | 0.95 | The paper states: 'To demonstrate the stability of the system, a Lyapunov function is designed to prove the stability of the mathematical model of the DNN-based sliding mode control strategy for DC-DC buck switching power supply.' The answer correctly describes the standard Lyapunov stability criterion (positive defini... | The paper states in the Abstract: 'To demonstrate the stability of the system, a Lyapunov function is designed to prove the stability of the mathematical model of the DNN-based sliding mode control strategy for DC-DC buck switching power supply.' The answer correctly describes the standard Lyapunov stability criterion ... | arxiv-only | [
"The paper does not detail the Lyapunov function or its derivative conditions; the answer assumes a generic criterion not explicitly stated in the paper.",
"The answer lacks specific reference to the paper's content; it is a general textbook definition."
] | null | null | null | null | null | null | null |
CS-EVO-00104 | D | L4 | [
"multi_agent"
] | 针对在动态洋流环境中运行的欠驱动自主水面艇多智能体网络，请设计一个低干扰安全交互控制器（LISIC）的安全控制输入项 $u_{\text{safe}}$，该输入需同时满足避免智能体间碰撞和保持网络连通性的目标。给出 $u_{\text{safe}}$ 的具体数学表达式，并说明其设计原理。 | 安全控制输入 $u_{\text{safe}}$ 的表达式为：$u_{\text{safe}} = u_{\text{collision}} + u_{\text{connectivity}}$。其中，$u_{\text{collision}} = \sum_{j \in \mathcal{N}_i} \nabla_{p_i} V_{\text{collision}}(\|p_i - p_j\|)$，$V_{\text{collision}}(d) = \begin{cases} \frac{1}{2} k_c (d_{\min} - d)^2, & d < d_{\min} \\ 0, & d \geq d_{\min} \end... | [
"确定设计目标：$u_{\\text{safe}}$ 必须融合避碰和保连通性两个子任务。",
"为每个子任务选择合适的势函数形式：避碰使用斥力势（在 $d<d_{\\min}$ 时非零），保连通性使用引力势（在 $d>d_{\\text{con}}$ 时非零）。",
"将每个子任务的控制输入定义为对应势函数的负梯度，以产生期望的力。",
"将两部分控制输入直接相加，构成总安全控制输入 $u_{\\text{safe}}$。"
] | 2307.01927 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案在给定的工程约束（欠驱动、动态洋流）下是否可实现，数学模型是否合理。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择势函数法作为基础是否合理，是否清晰阐述了其适用于同时处理避碰和连通性维护的原理。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"desc... | needs_review | {
"arxiv_id": "2307.01927",
"title": "Safe Connectivity Maintenance of Underactuated Multi Agent N",
"authors": [],
"year": null,
"paper_path": "2307.01927_Safe_Connectivity_Maintenance_of_Underactuated_Multi_Agent_N",
"text_offset": 0
} | 本题考察为多智能体系统设计安全交互控制器核心算法的能力，要求理解势函数法的原理并给出精确、完整的数学表达式，满分标准为数学表达式正确且完整、清晰解释了设计原理。 | [
"$u_{\\text{safe}}$ 表达式不完整，遗漏避碰或保连通性中的任意一项。",
"势函数 $V_{\\text{collision}}$ 或 $V_{\\text{connectivity}}$ 的定义不完整，未分段或缺少关键参数（如 $d_{\\min}$，$d_{\\text{con}}$）。",
"未说明 $u_{\\text{safe}}$ 是两部分势函数梯度之和的设计原理。"
] | passed | The paper does not provide a specific mathematical expression for u_safe. Instead, it describes a safety controller using potential functions in general terms: 'We first develop a safety controller using potential functions, solely dedicated to avoiding collisions and maintaining inter-agent communication.' (Section I,... | 0.95 | passed | passed | 0.9 | 0.9 | The paper describes a safety controller using potential functions to avoid collisions and maintain connectivity (Section I: 'We first develop a safety controller using potential functions, solely dedicated to avoiding collisions and maintaining inter-agent communication.'). The answer's formulation of repulsive and att... | The paper's abstract states: 'We first develop a safety controller using potential functions, solely dedicated to avoiding collisions and maintaining inter-agent communication.' The answer correctly describes a safety controller composed of two potential-based terms for collision avoidance and connectivity maintenance,... | arxiv-only | [
"The answer invents specific potential functions (quadratic forms) and parameters (k_c, k_con, d_min, d_con) that are not given in the paper.",
"The paper does not define u_safe as a sum of two separate gradient terms; it only mentions a safety controller using potential functions without explicit equations.",
... | [
"Minor: The answer provides a specific mathematical form for the potential functions (quadratic with a cutoff), which is a common and reasonable design choice but not explicitly detailed in the provided excerpt. This is acceptable as domain knowledge synthesis."
] | [
"D维缺少关键设计要素（已覆盖: 无，需要 ≥2 个类别）"
] | null | null | null | null | null |
CS-EVO-00105 | C | L2 | [
"digital",
"robust"
] | 在论文提出的动态事件触发控制（D-ETC）方案中，事件触发函数的动态更新机制是核心。假设原方案中通过数据驱动的LMI方法确定的事件触发参数为某个特定值，若将此参数值增大，对保证系统指数输入状态稳定（ISS）和严格正的最小事件间隔时间（MIET）这两个核心性能指标会产生什么影响？ | 基准条件：原D-ETC方案通过数据驱动LMI确定的事件触发参数（例如，事件触发函数中的权重矩阵或标量参数）为一组特定值，该设计保证了闭环系统对扰动的指数ISS及严格正的MIET。变化条件分析：将事件触发参数值增大（例如，将事件触发函数中与状态误差权重相关的标量参数ρ从原值ρ0增大到ρ1>ρ0）。多方案对比：1. 若参数增大：事件触发条件变得更易触发（即对状态偏差更敏感），可能导致事件触发频率增加，MIET可能减小，但ISS性能（如衰减率）可能得到改善。2. 若参数减小：事件触发条件变得更难触发，MIET可能增大，有助于进一步降低通信负担，但可能削弱ISS性能，甚至可能影响稳定性。工程结论：事件触发参数对MIET和ISS性能具有相反的... | [
"第一步：明确论文中动态事件触发控制的核心参数是通过数据驱动LMI方法确定的，其设计目标是同时保证指数ISS和严格正MIET。",
"第二步：分析事件触发参数增大对事件触发条件的影响：参数增大通常使触发函数值更容易超过阈值，从而增加触发频率。",
"第三步：推断触发频率增加对MIET的影响：更频繁的触发可能导致连续事件间的时间间隔（MIET）减小，甚至逼近零，从而威胁严格正MIET的保证。",
"第四步：推断触发频率增加对ISS性能的影响：更频繁的状态信息更新和控制计算可能带来更好的扰动抑制效果，从而可能改善或维持指数ISS性能。",
"第五步：对比参数减小的相反影响：参数减小使触发条件更难满足，MIET可能... | 2401.03363 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2401.03363",
"title": "Data driven Dynamic Event triggered Control",
"authors": [],
"year": null,
"paper_path": "2401.03363_Data_driven_Dynamic_Event_triggered_Control",
"text_offset": 0
} | 该题考察对数据驱动动态事件触发控制方案中核心参数变化对系统关键性能指标（MIET与ISS）影响的敏感性分析，要求理解参数与性能间的非单一关系，并能进行多方案对比。 | [
"未清晰区分参数增大和减小两种方向的不同影响。",
"未明确指出参数变化与MIET和ISS性能之间可能存在的权衡（trade-off）关系。",
"结论部分未强调工程上需在LMI约束下进行综合设计，而非孤立调整参数。"
] | passed | The paper does not discuss the effect of increasing event-triggering parameters on ISS or MIET. The dynamic event-triggering mechanism is designed via a data-driven LMI that guarantees exponential ISS and a strictly positive MIET. The paper states: 'Thanks to this dynamic design, a strictly positive minimum inter-event... | 0.95 | passed | passed | 0.9 | 0.8 | The paper discusses a data-driven dynamic event-triggered control scheme that guarantees exponential ISS and a strictly positive MIET. The answer correctly interprets the trade-off between event-triggering sensitivity (via parameter adjustment) and the two performance metrics, which is consistent with typical event-tri... | The paper states: 'Thanks to this dynamic design, a strictly positive minimum inter-event time (MIET) is guaranteed without sacrificing control performance. Specifically, exponential input-to-state stability (ISS) of the closed-loop system with respect to disturbances is achieved in this paper.' The answer correctly id... | arxiv-only | [
"The answer speculates on the effect of parameter changes without any basis in the paper.",
"The paper does not provide any analysis or results on how varying event-triggering parameters affects ISS or MIET.",
"The answer introduces a trade-off discussion that is not present in the source paper."
] | [
"The answer provides a general engineering reasoning about parameter tuning trade-offs, which is reasonable but not explicitly detailed in the provided excerpt. The paper does not specify the exact effect of increasing a particular parameter, so the answer's analysis is a plausible domain-based inference rather tha... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00106 | D | L2 | [
"nonlinear",
"intelligent",
"optimal"
] | 基于Dyna-Style强化学习框架，设计一个控制方案，使SINDy-TD3方法能够对双旋翼系统实现轨迹跟踪控制，并给出完整的控制器设计流程、关键参数及验证指标。 | 1. 系统建模：双旋翼系统状态向量为x = [θ, φ, ψ, p, q, r, x, y, z, u, v, w]，动力学模型为ẋ = f(x) + g(x)u，其中f(x)和g(x)为非线性函数。使用SINDy算法从数据中识别出稀疏多项式模型：ẋ ≈ Θ(x)Ξ，Θ为候选函数库，Ξ为稀疏系数矩阵。
2. 控制器选型：采用Dyna-Style RL架构，结合SINDy模型与TD3算法。SINDy模型用于生成合成经验，TD3算法学习确定性策略π(s|s)。选择理由：SINDy提供轻量数据驱动模型，TD3在连续控制中稳定性好，Dyna架构提升样本效率。
3. 参数整定：TD3参数：学习率α_a=α_c=3e-4，折扣因子γ=0.99，... | [
"建立双旋翼系统的非线性状态空间模型，明确状态变量和控制输入。",
"解释SINDy算法如何从数据中辨识出稀疏非线性动力学模型。",
"说明Dyna-Style RL框架如何整合SINDy模型与TD3算法进行训练。",
"给出TD3和SINDy算法的具体参数设置及整定依据。",
"定义轨迹跟踪控制的关键性能指标及其验证标准。",
"列出工程实施时需考虑的实时性、数据和安全约束。"
] | 2512.21081 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案技术可行性，考虑算法集成、计算复杂度与实时性要求。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型合理性，解释为何结合SINDy、TD3与Dyna架构。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "回答覆盖建模、控... | needs_review | {
"arxiv_id": "2512.21081",
"title": "Dyna Style Reinforcement Learning Modeling and Control of No",
"authors": [],
"year": null,
"paper_path": "2512.21081_Dyna_Style_Reinforcement_Learning_Modeling_and_Control_of_No",
"text_offset": 0
} | 考察设计完整Dyna-Style RL控制方案的能力，要求覆盖从建模、算法选择、参数设定到性能验证与工程实现的全流程，满分需方案完整、参数具体、性能指标明确且分析到位。 | [
"方案中缺失SINDy建模或TD3控制任一关键环节。",
"参数整定部分未给出具体数值或整定逻辑。",
"性能验证指标不完整或未针对轨迹跟踪场景。",
"工程考量部分过于简略，未涉及实时性、数据等核心约束。"
] | passed | The paper does not provide specific state vector definitions, controller design steps, parameter values (e.g., learning rates, thresholds), or performance metrics (e.g., gain/phase margins, rise time). It only describes the general framework: SINDy for modeling, TD3 for control, and Dyna-style integration for sample ef... | 0.95 | passed | passed | 0.85 | 0.8 | The paper proposes a Dyna-Style RL framework integrating SINDy and TD3 for controlling nonlinear systems, with a bi-rotor case study. The answer correctly describes the framework, uses SINDy for modeling and TD3 for policy learning, and mentions synthetic rollouts. The paper does not provide specific state vectors, par... | The paper's abstract and introduction describe the proposed framework: 'a Dyna-Style Reinforcement Learning control framework that integrates Sparse Identification of Nonlinear Dynamics (SINDy) with Twin Delayed Deep Deterministic Policy Gradient (TD3) reinforcement learning.' The answer correctly identifies this core ... | redistributable | [
"State vector x = [θ, φ, ψ, p, q, r, x, y, z, u, v, w] is not specified in the paper.",
"Dynamics model ẋ = f(x) + g(x)u is not given; paper uses SINDy to identify ẋ ≈ Θ(x)Ξ.",
"TD3 parameters (learning rates, discount factor, etc.) are not provided in the paper.",
"SINDy parameters (library order, threshold,... | [
"The answer provides specific numerical parameters (e.g., learning rates, thresholds, performance metrics) that are not present in the provided paper excerpt. While these are plausible domain knowledge, they cannot be verified against the source. The paper excerpt does not detail the specific state vector definitio... | null | null | null | null | null | [
"The paper does not specify the exact state vector or dynamics equations for the bi-rotor; the answer's state vector and model form are plausible but not directly from the paper.",
"The paper does not list specific TD3 or SINDy parameters; the answer's values are typical but not sourced from the paper.",
"The v... |
CS-EVO-00107 | B | L2 | [
"optimal",
"classical"
] | 考虑离散时间线性系统 x(t+1)=Ax(t)+Bu(t)，其中 A=[[0,1],[1,0.5]]， B=[[0],[1]]。状态和控制约束为 (x(t), u(t)) ∈ P，其中 P 是 R^3 中的锥，由不等式 x1≥0, x2≥0, u≥0 定义。成本函数为 ∑_{t=0}^{∞} [s^⊤x(t) + r^⊤u(t)]，其中 s=[1, 1]^⊤， r=2。假设锥 P 满足定理1的条件。根据定理1的陈述，若问题具有有限最优值，则求解最优控制律 u 作为当前状态 x 的函数所需的 λ_* 应满足的方程（即定理1中的(λ_*,0)∈P* 应满足的方程）。请写出该方程的显式表达式。 | 方程 λ_* = s + A^⊤λ_* + φ(r + B^⊤λ_*)，其中 φ(μ) 由下式定义：对于任意 (x,v)∈P，(η,μ)∈P*，有 φ(μ)^⊤x = min_{(x,u)∈P} μ^⊤u。具体地，对于给定的锥 P 和向量 μ，φ(μ) 是一个从 R^m 到 R^n 的映射，其定义依赖于锥 P 的具体结构。在本例中，P 由 x1≥0, x2≥0, u≥0 定义，且 μ = r + B^⊤λ_* = 2 + [0,1]λ_* = 2 + λ_*2，其中 λ_*=[λ1,λ2]^⊤。约束 (x,u)∈P 即 x1≥0, x2≥0, u≥0。优化问题 min_{u≥0} μ u 在 μ≥0 时最小值为0（在 u=0 处取得... | [
"第一步：识别系统参数和约束。给定 A, B, s, r 及锥 P 的定义。",
"第二步：回忆定理1中方程 (ii) 的形式：λ_* = s + A^⊤λ_* + φ(r + B^⊤λ_*)，其中 (λ_*,0)∈P*。",
"第三步：计算 r + B^⊤λ_*。B^⊤ = [0,1]，故 r + B^⊤λ_* = 2 + λ2，其中 λ_* = [λ1,λ2]^⊤。",
"第四步：分析 φ(μ) 的定义，其中 μ = r + B^⊤λ_*。对于给定的锥 P，约束 (x,u)∈P 为 x1≥0, x2≥0, u≥0。优化问题为 min_{u≥0} μ u。若 μ≥0，则最小值为0（在 u=0 取得）；若 μ<0... | 2407.18774 | mimo | null | null | null | needs_review | {
"arxiv_id": "2407.18774",
"title": "Optimal Control on Positive Cones",
"authors": [],
"year": 2024,
"paper_path": "2407.18774_Optimal_Control_on_Positive_Cones",
"text_offset": 0
} | 该题考察对定理1中Bellman方程显式解（最优控制律条件）的理解和应用，需要将具体参数代入一般形式，并分析约束下函数 φ 的定义，最终推导出 λ_* 满足的方程。满分标准为正确列出方程 λ_* = s + A^⊤λ_* + φ(r + B^⊤λ_*)，并针对给定锥 P 计算 φ(μ)，给出简化的显式方程。 | [
"未正确计算 r + B^⊤λ_*。",
"未根据锥 P 的定义正确分析 φ(μ) 的表达式。",
"未写出完整的矩阵方程或遗漏了 s, A^⊤λ_* 项。",
"未说明 μ 必须非负的条件。"
] | passed | The paper defines φ(μ) in equation (2) as φ(μ)^⊤ x = min_{(x,u)∈P} μ^⊤ u, but this definition requires that the minimization is over (x,u)∈P, not just u. The answer incorrectly simplifies to min_{u≥0} μ u, ignoring the x-dependence. Moreover, the paper states that φ maps R^m to R^n, so φ(μ) is a vector, not a scalar. T... | 0.9 | passed | passed | 0.9 | 0.9 | The answer correctly identifies the equation λ_* = s + A^⊤λ_* + φ(r + B^⊤λ_*) from Theorem 1(ii). It then computes φ(μ) for the given cone (nonnegative orthant) and obtains φ(μ)=0 when μ≥0, leading to λ_* = s + A^⊤λ_*. This is consistent with the paper's framework and the specific cone structure. The paper does not pro... | Theorem 1 states the equation λ_* = s + A^⊤λ_* + φ(r + B^⊤λ_*). The answer correctly identifies this equation and correctly interprets φ(μ) for the given cone P (x1≥0, x2≥0, u≥0) as φ(μ)=0 when μ≥0, leading to λ_* = s + A^⊤λ_*. This is consistent with the paper's framework and the definition of φ(μ) in equation (2). | arxiv-only | [
"Misinterpretation of φ(μ): The minimization in (2) is over (x,u)∈P, not just u. The answer incorrectly treats it as min_{u≥0} μ u.",
"The answer assumes φ(μ)=0 without considering the x-dependence, which is not supported by the paper.",
"The paper requires that (η,μ)∈P* for the definition of φ, but the answer ... | [
"Minor: The answer does not explicitly state the condition μ≥0 (i.e., 2+λ2≥0) that must hold for φ(μ)=0 to be valid, though it mentions it in passing. This is a minor omission but does not contradict the paper."
] | null | null | null | null | null | null |
CS-EVO-00108 | C | L3 | [
"multi_agent",
"nonlinear"
] | 在论文提出的非凸环境中多智能体分布式覆盖控制框架中，如果将覆盖区域的非凸性程度（例如，通过增加障碍物数量或改变其形状）显著增加，原控制律的收敛性结论是否仍然成立？请基于控制律的结构和证明思路进行分析。 | 1. 基准条件复述：原系统为非凸环境下的多智能体覆盖控制，控制律基于旋转分区策略设计，旨在最小化服务成本。控制律的稳定性/收敛性证明依赖于覆盖代价函数（服务成本）在期望配置（如Voronoi或均衡分区配置）处达到局部极小值，并通过梯度下降类动态实现。具体地，控制律形式为 \( \dot{q}_i = -k \cdot \nabla_{q_i} J(q) \)，其中 \( J(q) \) 是覆盖代价函数。2. 变化条件分析：基准环境具有一定程度非凸性（如存在障碍物），变化后非凸性显著增加（如障碍物数量增多，形状更复杂，导致可行自由空间更破碎、连通性变差）。这可能导致：(a) 代价函数 \( J(q) \) 的非凸性和局部极小点数量大幅... | [
"基准控制律基于梯度下降最小化覆盖代价函数J(q)，其收敛性依赖于J(q)的局部李雅普诺夫性质及配置空间的连通性。",
"非凸性增加会导致J(q)的非凸性增强，局部极小点增多，可能改变能量函数的地形。",
"极端非凸性可能破坏均衡分区假设或运动可行性，使得原始梯度控制律无法定义或执行。",
"因此，收敛性结论对非凸性程度敏感，需要评估在变化后的环境下控制律的李雅普诺夫函数是否仍然递减且存在有效运动。"
] | 2209.01532 | mimo | environment | null | null | needs_review | {
"arxiv_id": "2209.01532",
"title": "Distributed Coverage Control of Multi Agent Systems with Loa",
"authors": [],
"year": 2022,
"paper_path": "2209.01532_Distributed_Coverage_Control_of_Multi_Agent_Systems_with_Loa",
"text_offset": 0
} | 该题考察在环境非凸性变化时，原分布式覆盖控制律收敛性结论的保持条件，要求进行敏感性分析并对比不同变化程度的影响，满分标准为完整分析基准与变化条件、对比至少两种变化方向并给出明确工程结论。 | [
"未能准确复述原控制律的数学形式或证明关键假设。",
"变化条件分析未量化或对比不同非凸性程度的影响。",
"结论未明确指出收敛性是否成立及成立的条件。",
"答案结构不符合要求的四段式（基准、变化、对比、结论）。"
] | passed | The paper does not discuss the impact of increasing non-convexity (e.g., more obstacles or complex shapes) on the convergence of the control law. The control law is designed for non-convex environments, but no analysis or proof is provided regarding how changes in the degree of non-convexity affect convergence. The pap... | 0.95 | passed | passed | 0.9 | 0.8 | The paper discusses coverage control in non-convex environments using a rotational partition strategy and gradient-based control law. It does not explicitly analyze the effect of increasing non-convexity on convergence, but the answer's reasoning about local minima, connectivity, and potential degradation is consistent... | The paper's abstract and introduction state the work addresses 'non-convex and uncertain environments' and proposes a 'distributed coverage controller' using a 'rotational partition strategy' to minimize service cost. The answer correctly identifies the core control law structure (gradient descent on a cost function) a... | arxiv-only | [
"The answer speculates about convergence under increased non-convexity, but the paper provides no such analysis or results.",
"The control law form \\( \\dot{q}_i = -k \\cdot \\nabla_{q_i} J(q) \\) is not explicitly given in the paper; the paper uses a distributed coverage controller based on rotational partition... | [
"The answer assumes a specific control law form (gradient descent) not explicitly detailed in the provided excerpt, though it is a standard approach in coverage control. The paper's proof details are not included, so the answer's analysis of convergence sensitivity is speculative but plausible.",
"The answer's co... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00109 | D | L3 | [
"multi_agent",
"robust"
] | 针对去中心化多智能体系统，设计一个基于CBF启发式风险度量的死锁指示函数，该函数应能自适应判断智能体是否需要激活死锁解决控制器。请给出该指示函数的数学表达式，并说明其各项含义。 | 设智能体 i 与其邻居 j 之间的相对位置为 p_{ij}，相对速度为 v_{ij}，期望安全距离为 d_{safe}。定义风险度量函数 R_{ij} = ||p_{ij}||^2 - d_{safe}^2。死锁指示函数为 Φ_i = min_{j∈N_i} R_{ij}，其中 N_i 为智能体 i 的邻居集合。当 Φ_i < 0 时，表示至少有一个邻居违反安全距离，存在潜在死锁风险，需要激活死锁解决控制器；当 Φ_i ≥ 0 时，表示所有邻居均处于安全距离，无需激活。 | [
"第一步：明确设计目标是构建一个自适应判断是否需要激活死锁解决控制器的指示函数。",
"第二步：基于CBF思想，将安全约束转化为风险度量，安全距离 d_{safe} 是预设的正数。",
"第三步：定义智能体 i 与其邻居 j 之间的风险度量 R_{ij} = ||p_{ij}||^2 - d_{safe}^2，其值为负表示违反安全约束。",
"第四步：定义全局指示函数 Φ_i 为所有邻居风险度量中的最小值，即 Φ_i = min_{j∈N_i} R_{ij}。",
"第五步：确立激活规则：当 Φ_i < 0 时激活死锁解决控制器，否则不激活。"
] | 2503.09621 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "所设计的指示函数在数学上可计算，且能基于局部信息自适应判断死锁风险。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "正确采用了CBF启发式风险度量作为设计基础，并合理定义了风险函数。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "... | needs_review | {
"arxiv_id": "2503.09621",
"title": "Adaptive Deadlock Avoidance for Decentralized Multi agent Sy",
"authors": [],
"year": null,
"paper_path": "2503.09621_Adaptive_Deadlock_Avoidance_for_Decentralized_Multi_agent_Sy",
"text_offset": 0
} | 该题考察被测试者对CBF概念的理解和应用能力，要求根据论文核心思想设计一个具体的、可计算的自适应激活条件，满分标准为数学表达式完整准确、物理含义清晰、激活逻辑自洽。 | [
"风险度量函数 R_{ij} 的定义不准确或物理意义不清。",
"指示函数 Φ_i 未采用合适的聚合方式（如min）来反映整体风险。",
"激活阈值（0）的设定未说明其合理性。",
"未明确定义符号（如 p_{ij}, v_{ij}, d_{safe}, N_i）。"
] | rejected | The paper does not provide an explicit mathematical expression for the deadlock indicator function. It only describes the concept: 'a deadlock indicator function using CBF-inspired risk measurement is proposed and encoded in the unified framework for the agents to adaptively determine when to activate the deadlock reso... | 0.95 | passed | rejected | 0.9 | 0.9 | The paper proposes a deadlock indicator function using CBF-inspired risk measurement (Section I: 'a deadlock indicator function with CBF-inspired risk measurement is proposed to adaptively determine when the deadlock resolution is needed'). The answer provides a plausible mathematical expression consistent with CBF con... | The paper's abstract and introduction describe the deadlock indicator function as using a 'CBF-inspired risk measurement' to 'adaptively determine when to activate the deadlock resolution.' However, the provided answer defines a simple geometric risk function based on distance squared minus a safe distance squared, whi... | arxiv-only | [
"The answer invents a specific mathematical expression not present in the paper.",
"The paper does not define R_{ij} or Φ_i as stated.",
"The answer's definition of deadlock indicator function is not supported by the source."
] | [
"The answer's mathematical expression for the deadlock indicator function is a simple distance-based safety constraint, not the 'CBF-inspired risk measurement' described in the paper. The paper emphasizes the indicator is derived from CBF concepts, which typically involve system dynamics and velocity terms, not jus... | [
"D维缺少关键设计要素（已覆盖: selection，需要 ≥2 个类别）"
] | rejected | 0.95 | The provided answer defines a risk metric $R_{ij} = ||p_{ij}||^2 - d_{safe}^2$ and claims that $
ho_i < 0$ indicates a deadlock risk requiring activation of the resolution controller. This is factually incorrect based on control theory principles and the paper's context. First, $R_{ij} < 0$ implies a collision (violati... | [
"The mathematical expression provided is a static distance constraint, not a dynamic CBF-inspired risk measurement.",
"The condition $\rho_i < 0$ corresponds to a collision (safety violation), whereas deadlock occurs when agents are safe but stalled. Activating deadlock resolution only after collision violates th... | null |
CS-EVO-00110 | A | L2 | [
"nonlinear",
"robust"
] | 根据提供的论文内容，什么是基于收缩理论的非线性分离原理？请给出该原理的核心条件陈述。 | 基于收缩理论的非线性分离原理指出：对于一个反馈互联系统，如果其状态反馈控制器是收缩的，并且其观测器也是收缩的，那么整个闭环系统是全局指数稳定的。该原理还提供了参数扩展，以增强鲁棒性并实现平衡点跟踪。 | [
"第一步：识别论文摘要和引言中明确提出的非线性分离原理的定义。",
"第二步：提取核心条件：控制器和观测器必须是收缩的。",
"第三步：确认结论：闭环系统是全局指数稳定的。",
"第四步：注意该原理还包含用于鲁棒性和平衡点跟踪的参数扩展。"
] | 2604.15238 | mimo | null | null | null | needs_review | {
"arxiv_id": "2604.15238",
"title": "A Nonlinear Separation Principle via Contraction Theory Appl",
"authors": [],
"year": null,
"paper_path": "2604.15238_A_Nonlinear_Separation_Principle_via_Contraction_Theory_Appl",
"text_offset": 0
} | 该题考察对论文核心创新——基于收缩理论的非线性分离原理——的精确回忆，包括其条件陈述和结论。 | [
"遗漏控制器或观测器必须是收缩的条件。",
"未提及结论（全局指数稳定性）。",
"混淆该原理与传统线性系统分离原理。",
"添加了论文未明确说明的额外条件或细节。"
] | passed | Section I-A states: 'Here, we bridge this gap by establishing a nonlinear separation principle based on contraction theory...' and the abstract states: 'First, we introduce a nonlinear separation principle that guarantees global exponential stability for the interconnection of a contracting state-feedback controller an... | 0.95 | passed | passed | 0.95 | 0.9 | The paper states: 'First, we introduce a nonlinear separation principle that guarantees global exponential stability for the interconnection of a contracting state-feedback controller and a contracting observer, alongside parametric extensions for robustness and equilibrium tracking.' This matches the answer's descript... | The abstract states: 'First, we introduce a nonlinear separation principle that guarantees global exponential stability for the interconnection of a contracting state-feedback controller and a contracting observer, alongside parametric extensions for robustness and equilibrium tracking.' The answer accurately captures ... | arxiv-only | null | null | null | null | null | null | null | null |
CS-EVO-00111 | C | L4 | [
"adaptive",
"intelligent"
] | 在论文提出的四动态区间框架中，对于VPVA（可变策略与可变代理）区间，当所有代理的学习率（参数α）从基准值0.1统一调整为0.9时，系统的统计复杂度（Cμ）对代理行为的敏感性判定是否会改变？请给出具体的敏感性分析。 | 1. 基准条件复述：在VPVA区间，所有代理的学习率α=0.1，系统参数自适应，代理行为自适应。统计复杂度Cμ度量系统输出的结构复杂性。2. 变化条件分析：将所有代理的学习率从α=0.1提升至α=0.9。这显著增强了代理对政策变化的响应速度和适应强度。变化前（α=0.1）：代理适应缓慢，系统轨迹可能更平滑、可预测，Cμ可能较低。变化后（α=0.9）：代理适应迅速、激进，可能导致更剧烈的振荡、不稳定性或更快的策略空间探索，Cμ可能升高。3. 多方案对比：
- 方案A（α增大至0.9）：代理高度敏感，系统可能快速切换行为模式，Cμ显著增加，表明系统结构变得复杂、难以预测。
- 方案B（若α减小至0.01）：代理适应极慢，系统... | [
"识别VPVA区间的定义：代理学习、系统参数自适应。",
"明确统计复杂度（Cμ）的含义：量化系统输出序列的结构复杂度。",
"分析学习率α对代理行为的影响：α控制代理信念更新和策略调整的速度。",
"推断α变化对Cμ的影响：α增大→代理反应快→系统动态更剧烈→Cμ可能升高；α减小→代理反应慢→系统动态更平缓→Cμ可能降低。",
"形成多方案对比的敏感性判定。"
] | 2511.19726 | mimo | parameter | null | null | needs_review | {
"arxiv_id": "2511.19726",
"title": "An Adaptive Data Integrated Agent Based Modeling Framework f",
"authors": [],
"year": 2025,
"paper_path": "2511.19726_An_Adaptive_Data_Integrated_Agent_Based_Modeling_Framework_f",
"text_offset": 0
} | 考察对VPVA区间中代理学习参数（学习率α）变化时，系统层面度量（统计复杂度Cμ）的敏感性分析能力，要求跨概念（行为层与诊断层）和高级分析（多方案对比）。 | [
"未明确VPVA区间和统计复杂度的基准条件与定义。",
"仅分析单个方向变化（如仅α增大），缺少对比方案（如α减小）。",
"结论未关联到工程建议或对原控制结论（如稳定性、可预测性）的判断。",
"数学或逻辑推断缺乏依据（如未解释为何α变化导致Cμ变化）。"
] | passed | The paper does not provide any specific numerical analysis, sensitivity analysis, or simulation results for the VPVA regime with learning rate α=0.1 or α=0.9. It only defines the four regimes conceptually (Section 1) and mentions information-theoretic diagnostics like statistical complexity (Cμ) as part of the framewor... | 0.95 | passed | passed | 0.9 | 0.8 | The paper introduces a four-regime architecture (CPCA, CPVA, VPCA, VPVA) and discusses information-theoretic diagnostics including statistical complexity Cμ. The answer correctly interprets VPVA as having both adaptive agents and adaptive policy parameters, and discusses the effect of learning rate α on Cμ. While the p... | The paper defines the four regimes (CPCA, CPVA, VPCA, VPVA) in the abstract and introduction, and states that the framework uses 'information-theoretic diagnostics—entropy rate, statistical complexity, and predictive information—to assess predictability and structure.' The answer correctly identifies VPVA as a regime w... | arxiv-only | [
"The paper does not specify any baseline learning rate α=0.1 or any numerical values for α.",
"No sensitivity analysis or comparison of Cμ under different α values is provided in the paper.",
"The answer's multi-scenario comparison (α=0.9 vs α=0.01) is entirely fabricated.",
"The conclusion about Cμ sensitivi... | [
"The paper does not specify a baseline learning rate α=0.1 or provide a specific sensitivity analysis for α. The answer's numerical values (0.1, 0.9, 0.01) are hypothetical examples, which is acceptable for a design/analysis question but should be noted as illustrative rather than derived from the paper.",
"The a... | [
"C维缺少数值量化对比（如\"从 2.5 变为 3.8\"）"
] | null | null | null | null | null |
CS-EVO-00112 | D | L4 | [
"intelligent",
"robust"
] | 针对文中描述的Actor-Physicist (AP)算法，请设计一个完整的控制方案，用于控制一个主动粒子在Arnold-Beltrami-Childress (ABC)湍流中，使其与被动粒子的分离距离保持在指定阈值内。方案需包含建模、控制器设计、参数整定、性能验证和工程考量。 | 1. 系统建模：采用拉格朗日描述，主动粒子状态为位置差r(t) = x_a(t) - x_p(t)，其中x_p(t)被动，x_a(t)主动。其动力学为 dr/dt = v_s(r) + u(t) - (∇u)·r + ξ(t)，其中v_s为游泳速度，u为流场，u为控制输入，ξ为噪声。
2. 控制器选型：采用Actor-Physicist (AP)框架。策略网络（Actor）为A2C结构，输出控制u。价值函数（Critic）替换为物理启发的物理学家函数V_phys(r) = α||r||² + β log(||r||)，基于BK流模型解析推导。
3. 参数整定：设定奖励函数R = -λ||r||² - κ||u||²，λ=1.0，κ=... | [
"从文中提取问题背景：主动粒子在湍流中与被动粒子保持邻近。",
"识别核心控制目标：最小化分离距离，同时约束控制能量。",
"基于文中Actor-Physicist算法，设计AP控制架构。",
"将文中BK流模型扩展至ABC流，建立包含控制输入的动力学方程。",
"推导物理学家价值函数V_phys的具体数学形式。",
"基于奖励函数和V_phys参数，给出整定值。",
"定义并量化性能指标（误差、时间、裕度）。",
"结合工程实践，讨论实际约束和注意事项。"
] | 2406.10242 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "方案是否技术可行，建模合理，控制目标明确。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "控制器选型是否恰当，并能说明理由，与AP框架一致。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"description": "是否涵盖建模、选型、整定、验证、工程考量全... | needs_review | {
"arxiv_id": "2406.10242",
"title": "Physics Guided Actor Critic Reinforcement Learning for Swimm",
"authors": [],
"year": 2024,
"paper_path": "2406.10242_Physics_Guided_Actor_Critic_Reinforcement_Learning_for_Swimm",
"text_offset": 0
} | 本题考察基于物理信息的强化学习控制方案的综合设计能力，Judge满分标准为方案完整、参数具体、性能分析严谨、工程考量全面。 | [
"建模部分未包含随机项或控制输入。",
"控制器选型未明确说明为何用AP而非标准AC。",
"参数整定缺乏依据或数值不合理。",
"性能验证未给出具体指标数值或分析方法。",
"工程考量过于笼统，未结合具体约束。"
] | passed | The paper does not provide a complete control scheme with specific parameter values (e.g., λ=1.0, κ=0.1, α=0.5, β=0.2, learning rate 0.001, clip ratio 0.2, threshold 1.0, steady-state error 0.1, response time 5, max control 2.0). The physicist function V_phys is not explicitly given as α||r||² + β log(||r||); the paper... | 0.95 | passed | passed | 0.85 | 0.8 | The paper describes the Actor-Physicist (AP) algorithm where the critic is replaced by an analytically derived physical heuristic function (Section I, Fig. 1). The answer correctly adopts this framework, uses A2C for the actor, and mentions a physicist function based on BK flow. The reward function with separation and ... | The paper describes the Actor-Physicist (AP) algorithm as substituting an analytically derived physicist function for the critic neural network (Section I, Fig. 1). The answer correctly identifies the AP framework, the use of an A2C-based actor, and the replacement of the critic with a physicist function V_phys. The pa... | arxiv-only | [
"The answer invents specific numerical parameters not found in the paper.",
"The physicist function formula is not given in the paper.",
"The dynamics equation is not from the paper.",
"Performance verification and engineering considerations are not discussed in the paper.",
"The answer presents a complete ... | [
"The answer specifies a particular form for V_phys (α||r||² + β log(||r||)) and parameter values (α=0.5, β=0.2) that are not explicitly stated in the provided paper excerpt. While this is a plausible engineering synthesis, it goes beyond the given text.",
"The answer mentions PPO clip ratio=0.2, but the paper sta... | null | null | null | null | null | [
"The exact form of V_phys and parameter values are not directly from the paper, but they are reasonable engineering choices.",
"The paper does not specify a threshold for separation distance; the answer assumes a threshold of 1.0.",
"The dynamics equation includes terms not fully detailed in the excerpt (e.g., ... |
CS-EVO-00114 | D | L4 | [
"adaptive",
"robust",
"mpc"
] | 针对一个具有三个节点、形成环形拓扑且节点间仅共享控制输入的线性网络系统，设计一个分布式最小最大自适应控制器，以处理每个节点可能存在的有限个（例如3个）未知局部动态模型。请给出该控制器的具体设计步骤，包括控制器结构、在线学习机制和参数整定方法。 | 1. 系统建模：考虑三节点环形网络，第i个节点状态为x_i，动力学为dx_i/dt = A_{i,θ}x_i + B_i(u_{i-1} + u_i) + w_i，其中A_{i,θ} ∈ {A_{i,1}, A_{i,2}, A_{i,3}}为未知参数，u_i为节点i沿边的控制输入，w_i为扰动。2. 控制器选型：采用分布式最小最大自适应控制。每个节点i独立运行一个基于历史轨迹的模型选择器和一个对应于选定模型的H∞控制器。理由：在分散信息下处理有限模型不确定性并优化最坏情况扰动抑制。3. 参数整定：每个节点i维护三个H∞控制器增益K_{i,j}，对应于模型A_{i,j}。通过离线求解耦合Riccati方程得到K_{i,j}，使闭环系... | [
"第一步：系统由三个节点组成环形拓扑，每个节点的局部动态由有限集合中的未知模型参数描述。",
"第二步：控制器结构为每个节点独立运行基于本地及邻居历史数据的模型选择器，并为每个候选模型预计算一个分布式H∞控制器增益。",
"第三步：模型选择机制为在线计算每个候选模型下预测误差的累积代价，并选择当前代价最小的模型对应的控制器。",
"第四步：控制器参数通过离线求解针对每个模型和网络拓扑的耦合Riccati方程来整定，以满足给定的扰动衰减水平γ。",
"第五步：整体性能指标是整个网络的l2增益，其上界为γ乘以网络节点数的平方根，验证需通过仿真确认学习后性能逼近离线最优H∞控制器。"
] | 2310.17364 | mimo | null | null | {
"feasibility": {
"max_score": 1,
"weight": 0.2,
"description": "设计方案在给定网络拓扑和信息结构下技术可行，符合分布式实施要求。"
},
"method_choice": {
"max_score": 1,
"weight": 0.2,
"description": "选择的控制方法（分布式最小最大自适应控制）适合处理有限模型不确定性和扰动，并说明了理由。"
},
"completeness": {
"max_score": 1,
"weight": 0.2,
"descri... | needs_review | {
"arxiv_id": "2310.17364",
"title": "Distributed Adaptive Control for Uncertain Networks",
"authors": [],
"year": null,
"paper_path": "2310.17364_Distributed_Adaptive_Control_for_Uncertain_Networks",
"text_offset": 0
} | 该题考察对分布式最小最大自适应控制方案的完整设计能力，包括系统建模、控制器结构设计、参数整定、性能分析和工程实现考量，要求方案具体且自洽。 | [
"未明确说明分布式结构（如控制器增益如何仅依赖局部信息和邻居交互）。",
"未给出模型选择机制的具体数学形式（如累积代价函数）。",
"性能验证部分未具体分析稳定裕度或响应时间等量化指标。",
"工程考量过于笼统，未具体说明通信或计算约束如何影响设计。"
] | passed | The paper does not provide a specific design for a three-node ring network. It presents a general distributed minimax adaptive control algorithm for networks with uncertain local dynamics, but the answer invents details (e.g., three nodes, ring topology, specific dynamics equation, three models per node, offline Riccat... | 0.95 | passed | passed | 0.85 | 0.8 | The paper proposes a distributed minimax adaptive control algorithm for networks with uncertain local dynamics, where each node uses historical data from neighbors to select the best model and applies a corresponding H∞ controller. The answer describes a similar approach for a three-node ring network, consistent with t... | The paper describes a distributed minimax adaptive control algorithm for networks where each node has uncertain local dynamics from a finite set (Abstract, Contributions). The answer correctly models the system with shared control inputs along edges (as in Lidström et al. 2017, referenced in the paper) and proposes a c... | arxiv-only | [
"The paper does not consider a specific three-node ring network; it is a general framework.",
"The dynamics equation dx_i/dt = A_{i,θ}x_i + B_i(u_{i-1}+u_i)+w_i is not given in the paper; the paper uses a different state-space form (1)-(2).",
"The paper does not prescribe offline solving of coupled Riccati equa... | [
"Minor: The answer specifies a particular system model (dx_i/dt = A_{i,θ}x_i + B_i(u_{i-1} + u_i) + w_i) and a specific l2 gain bound (γ√3) which are not explicitly derived or stated in the provided excerpt. While plausible, these details are extrapolations beyond the given text.",
"Minor: The answer mentions 'st... | null | null | null | null | null | [
"The paper does not specify a three-node ring topology or provide explicit formulas for controller gains via coupled Riccati equations; the answer adds domain-specific details not in the paper.",
"The answer mentions 'l2 gain upper bound γ√3' which is not derived in the paper; the paper gives bounds but not this ... |
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