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2,400
An exact analysis of stable allocation
math.OC
Shapley and Scarf introduced a notion of stable allocation between traders and indivisible goods, when each trader has rank-ordered each of the goods. The purpose of this note is to prove that the distribution of ranks after allocation is the same as the distribution of search distances in uniform hashing, when the ran...
math
2,401
Two-way rounding
math.OC
Given $n$ real numbers $0\leq x_1,...,x_n<1$ and a permutation~$\sigma$ of $\{1,...,n\}$, we can always find $\xbar_1,...,\xbar_n\in\{0,1\}$ so that the partial sums $\xbar_1+... +\xbar_k$ and $\xbar_{\sigma 1}+... +\xbar_{\sigma k}$ differ from the unrounded values $x_1+... + x_k$ and $x_{\sigma 1}+... +x_{\sigma k}$ ...
math
2,402
Control of nonlinear underactuated systems
math.OC
In this paper we introduce a new method to design control laws for non-linear underactuated systems. Our method produces an infinite dimensional family of control laws, whereas most control techniques only produce a finite dimensional family. These control laws each come with a natural Lyapunov function. The inverted p...
math
2,403
Further results on controllability of recurrent neural networks
math.OC
This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of the result in the previous paper "Complete controllability of continuous-time recurrent neural networks" (Sontag and Sussmann) to a slightly different model, where inputs appear in an affine form...
math
2,404
Feedback Stabilization over Commutative Rings: Further study of the coordinate-free approach
math.OC
This paper is concerned with the coordinate-free approach to control systems. The coordinate-free approach is a factorization approach but does not require the coprime factorizations of the plant. We present two criteria for feedback stabilizability for MIMO systems in which transfer functions belong to the total rings...
math
2,405
A Tuner that Accelerates Parameters
math.OC
We propose a tuner, suitable for adaptive control and (in its discrete-time version) adaptive filtering applications, that sets the second derivative of the parameter estimates rather than the first derivative as is done in the overwhelming majority of the literature. Comparative stability and performance analyses are ...
math
2,406
Extremal Optimization: Methods derived from Co-Evolution
math.OC
We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization, successively eliminates extremely undesirable components of sub-optimal solutions, ra...
math
2,407
Games, predictions, interactivity
math.OC
This short note is devoted to the unraveling of the hidden interactivity of ordinary games which is an artefact of predictions of the behaviour of other players by the fixed player and describes deviations of their real behaviour from such predictions. A method to improve the predictions is proposed. Applications to th...
math
2,408
A Parameterization of Stabilizing Controllers over Commutative Rings
math.OC
We present a parameterization of the stabilizing controllers over commutative rings. In the classical case, that is, in the case where there exist the right-/left-coprime factorizations of the given plant, the stabilizing controllers can be parameterized by the method called ``Youla-Kucera-parameterization''. However, ...
math
2,409
Feedback Stabilization over Commutative Rings with no Right-/Left-Coprime Factorizations
math.OC
Anantharam showed in 1985 the existence of a model in which some stabilizable plants do not have its right-/left-coprime factorizations. In this paper, we give a condition of the nonexistence of the right-/left-coprime factorizations of stabilizable plants as a generalization of Anantharam's result. As examples of the ...
math
2,410
A method for computing quadratic Brunovsky forms
math.OC
In this paper, for continuous, linearly-controllable quadratic control systems with a single input, an explicit, constructive method is proposed for studying their Brunovsky forms, initially studied in [W. Kang and A. J. Krener, Extended quadratic controller normal form and dynamic state feedback linearization of nonli...
math
2,411
Mathematical Problems in the Control of Underactuated Systems
math.OC
In this paper we will discuss problems and techniques related to underactuated systems. We give a mathematical formulation of several problems arising from applications, review some standard and new techniques, and pose some interesting and challenging open questions.
math
2,412
Input-Output-to-State Stability
math.OC
This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence betwee...
math
2,413
Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in $H_\infty$ control
math.OC
This paper deals with the regularity of solutions of the Hamilton-Jacobi Inequality which arises in H-infinity control. It shows by explicit counterexamples that there are gaps between existence of continuous and locally Lipschitz (positive definite and proper) solutions, and between Lipschitz and continuously differen...
math
2,414
A Convex Maximization Problem: Discrete Case
math.OC
We study a specific convex maximization problem in n-dimensional space. The conjectured solution is proved to be a vertex of the polyhedral feasible region, but only a partial proof of local maximality is known. Integer sequences with interesting patterns arise in the analysis, owing to the number theoretic origin of t...
math
2,415
A Convex Maximization Problem: Continuous Case
math.OC
We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.
math
2,416
Elementary Factors and Reduced Minors for Linear Systems over Commutative Rings
math.OC
In 1994, Sule presented the necessary and sufficient conditions of the feedback stabilizability of systems over unique factorization domains in terms of elementary factors and in terms of reduced minors. Recently, Mori and Abe have generalized his theory over commutative rings. They have introduced the notion of the ge...
math
2,417
Matching control laws for a ball and beam system
math.OC
This note describes a method for generating an infinite-dimensional family of nonlinear control laws for underactuated systems. For a ball and beam system, the entire family is found explicitly.
math
2,418
Matching and digital control implementation for underactuated systems
math.OC
This note describes two problems related to the digital implementation of control laws in the infinite dimensional family of matching control laws, namely state estimation and sampled data induced error. The entire family of control laws is written for an inverted pendulum cart. Numerical simulations which include samp...
math
2,419
The fractional - order controllers: Methods for their synthesis and application
math.OC
This paper deals with fractional-order controllers. We outline mathematical description of fractional controllers and methods of their synthesis and application. Synthesis method is a modified root locus method for fractional-order systems and fractional-order controllers. In the next section we describe how to apply t...
math
2,420
The Calibration Method for Free Discontinuity Problems
math.OC
The calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems.
math
2,421
Matching, linear systems, and the ball and beam
math.OC
A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. This basic idea is used in several papers already. In this paper, we will describe one matching condition and an approach for finding all control laws that fit the ...
math
2,422
The modelling and analysis of fractional-order control systems in discrete domain
math.OC
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A practical example for modelling the fractional-order control loop is shown and obtained ...
math
2,423
Neural Stabilization/Excitation Control of a High-Order Power System by Adaptive Feedback Linearization
math.OC
This paper discusses the systematic design of an adaptive feedback linearizing neurocontroller for a high-order model of the synchronous machine/infinite bus power system. The power system is first modelled as an input-output nonlinear discrete-time system approximated by two neural networks. The approach allows a simp...
math
2,424
Output Feedback Control for Stabilizable and Incompletely Observable Nonlinear Systems
math.OC
This paper introduces a new approach for output feedback stabilization of SISO systems which, unlike most of the techniques found in the literature, does not use high-gain observers and control input saturation to achieve separation between the state feedback and observer designs. Rather, we show that by using nonlinea...
math
2,425
Output Feedback Control of Jet Engine Stall and Surge Using Pressure Measurements
math.OC
The problem of controlling surge and stall in jet engine compressors is of fundamental importance in preventing damage and lengthening the life of these components. In this paper, we use the Moore-Greitzer mathematical model to develop an output feedback controller for these two instabilities (only one of the three sta...
math
2,426
Modelling and analysis of fractional-order regulated systems in the state space
math.OC
In this paper we present the mathematical description and analysis of a fractional-order regulated system in the state space. A little historical background of our results in the analysis and synthesis of the fractional-order dynamical regulated systems is given. The methods and results of simulations of the fractional...
math
2,427
Control for a class of nonlinear systems with a time-varying structure
math.OC
In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by functions that depend on a possibly exogenous scheduling variable. We assume that each...
math
2,428
The modelling and analysis of fractional-order control systems in frequency domain
math.OC
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways for modelling of fractional-order systems are illustrated with a numerical example...
math
2,429
Partial synchronicity and the (max,+) semiring
math.OC
In this paper we illustrate how non-stochastic (max,+) techniques can be used to describe partial synchronization in a Discrete Event Dynamical System. Our work uses results from the spectral theory of dioids and analyses (max,+) equations describing various synchronization rules in a simple network. The network in que...
math
2,430
The simplest examples where the simplex method cycles and conditions where EXPAND fails to prevent cycling
math.OC
This paper introduces a class of linear programming examples which cause the simplex method to cycle indefinitely and which are the simplest possible examples showing this behaviour. The structure of examples from this class repeats after two iterations. Cycling is shown to occur for both the most negative reduced cost...
math
2,431
Iterated Local Search
math.OC
This is a survey of "Iterated Local Search", a general purpose metaheuristic for finding good solutions of combinatorial optimization problems. It is based on building a sequence of (locally optimal) solutions by: (1) perturbing the current solution; (2) applying local search to that modified solution. At a high level,...
math
2,432
Self-scaled barrier functions on symmetric cones and their classification
math.OC
Self-scaled barrier functions on self-scaled cones were introduced through a set of axioms in 1994 by Y.E. Nesterov and M.J. Todd as a tool for the construction of long-step interior point algorithms. This paper provides firm foundation for these objects by exhibiting their symmetry properties, their intimate ties with...
math
2,433
Integral-Input-Output to State Stability
math.OC
A notion of detectability for nonlinear systems is discussed. Within the framework of ``input to state stability'' (ISS), a dual notion of ``output to state stability'' (OSS), and a more complete detectability notion, ``input-output to state stability'' (IOSS) have appeared in the literature. This note addresses a vari...
math
2,434
Decomposition Algorithms for Stochastic Programming on a Computational Grid
math.OC
We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region method. The parallel platform of choice is the dynamic, heterogeneous, opportunisti...
math
2,435
Network Flow Optimization for Restoration of Images
math.OC
The network flow optimization approach is offered for restoration of grayscale and color images corrupted by noise. The Ising models are used as a statistical background of the proposed method. The new multiresolution network flow minimum cut algorithm, which is especially efficient in identification of the maximum a p...
math
2,436
On the lambda-equations for matching control laws
math.OC
We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely charactarized by a linear system of first order partial differential equations for one set of variables followed by a linear system of first order PDEs for a second set of variables. H...
math
2,437
On the Boundary Control of Systems of Conservation Laws
math.OC
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be ac...
math
2,438
Verification Theorems for Hamilton-Jacobi-Bellman equations
math.OC
We study an optimal control problem in Bolza form and we consider the value function associated to this problem. We prove two verification theorems which ensure that, if a function $W$ satisfies some suitable weak continuity assumptions and a Hamilton-Jacobi-Bellman inequality outside a countably $\mathcal H^n$-rectifi...
math
2,439
A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections
math.OC
A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable sys...
math
2,440
Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization
math.OC
The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of ...
math
2,441
Stability Rates for Patchy Vector Fields
math.OC
The paper is concerned with the stability of the set of trajectories of a vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. For patchy vector fields in the plane, with poly...
math
2,442
Asymptotic cauchy gains: Definitions and small-gain principle
math.OC
A notion of "asymptotic Cauchy gain" for input/output systems, and an associated small-gain principle, are introduced. A Lyapunov-like characterization allows the computation of these gains for state-space systems, and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in...
math
2,443
Vibrational control in H_infinity problems
math.OC
We consider the application of the theory of vibrational control to H_infinity-problems. We study the possibility of introduction of high-frequency parametric vibrations in order to decrease the minimal attainable value of the H_infinity-norm. We prove the existence of the stabilizing solution of the Riccati equation w...
math
2,444
Measurement to Error Stability: a Notion of Partial Detectability for Nonlinear Systems
math.OC
In previous work the notion of input to state stability (ISS) has been generalized to systems with outputs, yielding a number of useful concepts. When considering a system whose output is to be kept small (i.e. an error output), the notion of input to output stability (IOS) arises. Alternatively, when considering a sys...
math
2,445
Numerical Models for the Simulation of the Fractional-Order Control Systems
math.OC
This contribution deals with the creation of numerical models for the simulation of the dynamic characteristics of fractional-order control systems and their comparison with analytical models. We give the results of the comparison of dynamic properties in fractional- and integer-order systems with a controller, designe...
math
2,446
Identification of Fractional-Order Dynamical Systems
math.OC
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a discretization method and a numerical solution of differential equations of this...
math
2,447
State-Space Controller Design for the Fractional-Order Regulated System
math.OC
In this paper we will present a mathematical description and analysis of a fractional-order regulated system in the state space and the state-space controller design based on placing the closed-loop poles on the complex plane. Presented are the results of simulations and stability investigation of this system.
math
2,448
Fractional-Order State Space Models
math.OC
In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space for the integer-order and fractional-order system and the importance of the initia...
math
2,449
A remark on the converging-input converging-state property
math.OC
Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must also converge to the equilibrium. This "well-known" but hard-to-cite fact is prove...
math
2,450
Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems
math.OC
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain special properties. These properties are explored and are used in conjunction with the...
math
2,451
On the output-input stability property for multivariable nonlinear control systems
math.OC
We study the recently introduced notion of output-input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. The subject of this paper is developing the theory of output-input stability in the multi-input, multi-output setting. We show that output-input stabil...
math
2,452
Relaxation, New Combinatorial and Polynomial Algorithms for the Linear Feasibility Problem
math.OC
We consider the homogenized linear feasibility problem, to find an $x$ on the unit sphere, satisfying $n$ line ar inequalities $a_i^Tx\ge 0$. To solve this problem we consider the centers of the insphere of spherical simpl ices, whose facets are determined by a subset of the constraints. As a result we find a new combi...
math
2,453
Gradient algorithms for finding common Lyapunov functions
math.OC
This paper is concerned with the problem of finding a quadratic common Lyapunov function for a family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families.
math
2,454
Rational semimodules over the max-plus semiring and geometric approach of discrete event systems
math.OC
We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule S^n over a semiring S is rational if it has a generating family that is a r...
math
2,455
How to Evolve Safe Control Strategies
math.OC
Autonomous space vehicles need adaptive control strategies that can accommodate unanticipated environmental conditions. The evaluation of new strategies can often be done only by actually trying them out in the real physical environment. Consequently, a candidate control strategy must be deemed safe--i.e., it won't dam...
math
2,456
Exact Feedback Linearization of Stochastic Control Systems
math.OC
This paper studies exact linearization methods for stochastic SISO affine controlled dynamical systems. The systems are defined as vectorfield triplets in Euclidean space. The goal is to find, for a given nonlinear stochastic system, a combination of invertible transformations which transform the system into a controll...
math
2,457
A Remarkable Property of the Dynamic Optimization Extremals
math.OC
At the core of optimal control theory is the Pontryagin maximum principle - the celebrated first order necessary optimality condition - whose solutions are called extremals and which are obtained through a function called Hamiltonian, akin to the Lagrangian function used in ordinary calculus optimization problems. A re...
math
2,458
Lipschitzian Regularity of the Minimizing Trajectories for Nonlinear Optimal Control Problems
math.OC
We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of optimal trajectories, and the answer to it is crucial for closing the gap between t...
math
2,459
The Convergence of the Extended Kalman Filter
math.OC
We demonstrate that the extended Kalman filter converges locally for a broad class of nonlinear systems. If the initial estimation error of the filter is not too large then the error goes to zero exponentially as time goes to infinity. To demonstrate this, we require that the system be $C^2$ and uniformly observable wi...
math
2,460
Quantized control via locational optimization
math.OC
This paper studies state quantization schemes for feedback stabilization of control systems with limited information. The focus is on designing the least destabilizing quantizer subject to a given information constraint. We explore several ways of measuring the destabilizing effect of a quantizer on the closed-loop sys...
math
2,461
Multistability in Monotone I/O Systems, Preliminary Report
math.OC
We extend the setup in our previous paper to deal with the case in which more than one steady state may exist in feedback configurations. This provides a foundation for the analysis of multi-stability and hysteresis behaviour in high dimensional feedback systems.
math
2,462
Smoothed analysis of algorithms
math.OC
Spielman and Teng introduced the smoothed analysis of algorithms to provide a framework in which one could explain the success in practice of algorithms and heuristics that could not be understood through the traditional worst-case and average-case analyses. In this talk, we survey some of the smoothed analyses that ha...
math
2,463
A Globally Convergent LCL Method for Nonlinear Optimization
math.OC
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be reliable from arbitrary starting points. The well known example \MINOS\ has pro...
math
2,464
Gauge Symmetries and Noether Currents in Optimal Control
math.OC
We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a semi-invariance notion, and the transformation group may also depend on the control var...
math
2,465
On the problem of global optimisation of a multivariable function
math.OC
One of the actual problems in the field of numerical optimisation, as is well known, is the problem of the search for the global extremum of a multivariate function [1-9,13,14,17-21]. Various versions of the random search methods [6,8,9] are considered to be the most reliable to solve the problem of global optimisation...
math
2,466
A Semidefinite Representation for some Minimum Cardinality Problems
math.OC
Using techniques developed in [Lasserre02], we show that some minimum cardinality problems subject to linear inequalities can be represented as finite sequences of semidefinite programs. In particular, we provide a semidefinite representation of the minimum rank problem on positive semidefinite matrices. We also use th...
math
2,467
Quasi-Invariant Optimal Control Problems
math.OC
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are provided, in the direction which enlarges the scope of its application. We formulate...
math
2,468
The Lax conjecture is true
math.OC
In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov.
math
2,469
Matrosov's theorem using a family of auxiliary functions: an analysis tool to aid time-varying nonlinear control design
math.OC
We present a new result on uniform attractivity of the origin for nonlinear time-varying systems. Our theorem generalizes Matrosov's theorem which extends, in a certain manner, Krasovskii-LaSalle invariance principle to the case of general nonlinear time-varying systems. We show the utility of our theorem by addressing...
math
2,470
A catalog of inverse-kinematics planners for underactuated systems on matrix groups
math.OC
This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inverse-kinematics problems. We present a catalog of solutions for all underactuated systems on $\SE{2}$, $\SO{3}...
math
2,471
Exploring the capability and limits of the feedback mechanism
math.OC
Feedback is a most important concept in control systems, its main purpose is to deal with internal and/or external uncertainties in dynamical systems, by using the on-line observed information. Thus, a fundamental problem in control theory is to understand the maximum capability and potential limits of the feedback mec...
math
2,472
Global Asymptotic Controllability Implies Input to State Stabilization
math.OC
We study nonlinear systems with observation errors. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable with respect to actuator errors. Extensions for fully nonlinear GAC syst...
math
2,473
Positive forward rates in the maximum smoothness framework
math.OC
In this article we present a non-linear dynamic programming algorithm for the computation of forward rates within the maximum smoothness framework. The algorithm implements the forward rate positivity constraint for a one-parametric family of smoothness measures and it handles price spreads in the constraining dataset....
math
2,474
Digital Fractional Order Controllers Realized by PIC Microprocessor: Experimental Results
math.OC
This paper deals with the fractional-order controllers and their possible hardware realization based on PIC microprocessor and numerical algorithm coded in PIC Basic. The mathematical description of the digital fractional -order controllers and approximation in the discrete domain are presented. An example of realizati...
math
2,475
Comparison of the methods for discrete approximation of the fractional-order operator
math.OC
In this paper we will present some alternative types of discretization methods (discrete approximation) for the fractional-order (FO) differentiator and their application to the FO dynamical system described by the FO differential equation (FDE). With analytical solution and numerical solution by power series expansion...
math
2,476
Flexible Complementarity Solvers for Large-Scale Applications
math.OC
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set methods that solve only one linear system of equations per iteration. The linear sol...
math
2,477
A new conical internal evolutive LP algorithm
math.OC
In a previous paper, published in 1992, a primal conical LP algorithm with exact finite coonvergence was presented. The underlying optimality condition requires tangency of two sets (an affine space and a cone). In the algorithm the two sets remain disjoint until the last step. This left open the possibility of develop...
math
2,478
On the Constancy of the Pontryagin Hamiltonian for Autonomous Problems
math.OC
We provide a new, simpler, and more direct proof of the well known fact that for autonomous optimal control problems the Pontryagin extremals evolve on a level surface of the respective Pontryagin Hamiltonian.
math
2,479
A Harmonic Analysis Solution to the Static Basket Arbitrage Problem
math.OC
We consider the problem of computing upper and lower bounds on the price of a European basket call option, given prices on other similar baskets. We focus here on an interpretation of this program as a generalized moment problem. Recent results by Berg & Maserick (1984), Putinar & Vasilescu (1999) and Lasserre (2001) o...
math
2,480
Reachability problems for products of matrices in semirings
math.OC
We consider the following matrix reachability problem: given $r$ square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? We define similarly the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on...
math
2,481
The stochastic goodwill problem
math.OC
Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some ...
math
2,482
Nonlinear internal models for output regulation
math.OC
In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which we have presented in the recent paper entitled "Limit Sets, Zero Dynamics, and I...
math
2,483
Further Results on Lyapunov Functions and Domains of Attraction for Perturbed Asymptotically Stable Systems
math.OC
We present new theorems characterizing robust Lyapunov functions and infinite horizon value functions in optimal control as unique viscosity solutions of partial differential equations. We use these results to further extend Zubov's method for representing domains of attraction in terms of partial differential equation...
math
2,484
Bounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations, and Shape-From-Shading
math.OC
We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique bounded-from-below viscosity solution of the Hamilton-Jacobi equation which is null on the targ...
math
2,485
Uniform stability of damped nonlinear vibrations of an elastic string
math.OC
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is ...
math
2,486
Geometrical and Numerical Design of Structured Unitary Space Time Constellations
math.OC
In this paper we propose constellations with suitable structure which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods. We also demonstrate how these structured constellations out-perform currently existing constellations and explain why the proposed constellation s...
math
2,487
Pseudopolynomial algorithm for single machine scheduling (withdrawn)
math.OC
Withdrawn because of non-correctness. Would have implied too much to be true :-|
math
2,488
Bond Market Completeness and Attainable Contingent Claims
math.OC
A general class, introduced in [Ekeland et al. 2003], of continuous time bond markets driven by a standard cylindrical Brownian motion $\wienerq{}{}$ in $\ell^{2},$ is considered. We prove that there always exist non-hedgeable random variables in the space $\derprod{}{0}=\cap_{p \geq 1}L^{p}$ and that $\derprod{}{0}$ h...
math
2,489
Sublevel sets and global minima of coercive functionals and local minima of their perturbations
math.OC
The aim of the present paper is essentially to prove that if $\Phi$ and $\Psi$ are two sequentially weakly lower semicontinuous functionals on a reflexive real Banach space and if $\Psi$ is also continuous and coercive, then then following conclusion holds: if, for some $r > \inf_X \Psi$, the weak closure of the set $\...
math
2,490
Integral functionals on Sobolev spaces having multiple local minima
math.OC
In this paper, two multiplicity results about local minima of integrals of the calculus of variations are established. The main tool used to prove them is the theory developed in [B. Ricceri, Sublevel sets and global minima of coercive functionals and local minima of their pertubations, math.OC/0402444].
math
2,491
Discrete Nonlinear Observers for Inertial Navigation
math.OC
We derive an exact deterministic nonlinear observer to compute the continuous state of an inertial navigation system based on partial discrete measurements, the so-called strapdown problem. Nonlinear contraction is used as the main analysis tool, and the hierarchical structure of the system physics is sytematically exp...
math
2,492
On the Strong Invariance Property for Non-Lipschitz Dynamics
math.OC
We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the multifunction, we assume a feedback realization condition that can in particular be satisfied...
math
2,493
Common Polynomial Lyapunov Functions for Linear Switched Systems
math.OC
In this paper, we consider linear switched systems $\dot x(t)=A_{u(t)} x(t)$, $x\in\R^n$, $u\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\bf UAS} for short). We first prove that, given a {\bf UAS} system, it is always possible to build a common p...
math
2,494
On the existence of a common quadratic Lyapunov function for a rank one difference
math.OC
Suppose that A and B are real stable matrices, and that their difference A-B is rank one. Then A and B have a common quadratic Lyapunov function if and only if the product AB has no real negative eigenvalue. This result is due to Shorten and Narendra, who showed that it follows as a consequence of the Kalman-Yacubovich...
math
2,495
Reconsidering Conflict and Cooperation
math.OC
An analysis of several important aspects of competition or conflict in games, social choice and decision theory is presented. Inherent difficulties and complexities in cooperation are highlighted. These have over the years led to a certain marginalization of studies related to cooperation. The significant richness of c...
math
2,496
Generalized splines in R^n and optimal control
math.OC
We have found an inconsistency in our previous version of the paper "Generalized splines in R^n and optimal control". We give a new-time-dependent definition of spline curves in R^n which results from solving a non-autonomous linear quadratic optimal control problem (P) where the matrix B(t) is assumed to be rectangula...
math
2,497
Optimal Control of Volterra Equations with Impulses
math.OC
We consider an optimal control problem for a system governed by a Volterra integral equation with impulsive terms. The impulses act on both the state and the control; the control consists of switchings at discrete times. The cost functional includes both, an integrated cost rate (continuous part) and switching costs at...
math
2,498
Swarming Behavior of Multi-Agent Systems
math.OC
In this paper we consider a continuous-time anisotropic swarm model in $n$-dimensional space with an attraction/repulsion function and study its aggregation properties. It is shown that the swarm members will aggregate and eventually form a cohesive cluster of finite size around the swarm center. Moreover, the numerica...
math
2,499
Infinitesimal Characterizations for Strong Invariance and Monotonicity for Non-Lipschitz Control Systems
math.OC
We provide new infinitesimal characterizations for strong invariance of multifunctions in terms of Hamiltonian inequalities and tangent cones. In lieu of the standard local Lipschitzness assumption on the multifunction, we assume a new feedback realizability condition that can in particular be satisfied by control syst...
math