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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 |
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