Convex Computation of the Maximum Controlled Invariant Set For Polynomial Control Systems

We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and compact semialgebraic state and control constraints, we desc...

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Bibliographic Details
Published inSIAM journal on control and optimization Vol. 52; no. 5; pp. 2944 - 2969
Main Authors Korda, Milan, Henrion, Didier, Jones, Colin N.
Format Journal Article
LanguageEnglish
Published Society for Industrial and Applied Mathematics 01.01.2014
Subjects
Approximation
Control systems
Dynamical systems
Hierarchies
Invariants
Mathematics
Nonlinear dynamics
Optimization
Optimization and Control
Polynomials
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Summary:We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and compact semialgebraic state and control constraints, we describe a hierarchy of finite-dimensional linear matrix inequality (LMI) relaxations whose optimal values converge to the volume of the MCI set; dual to these LMI relaxations are sum-of-squares (SOS) problems providing a converging sequence of outer approximations to the MCI set. The approach is simple and readily applicable in the sense that the approximations are the outcome of a single semidefinite program with no additional input apart from the problem description. A number of numerical examples illustrate the approach.
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ISSN:0363-0129
1095-7138
DOI:10.1137/130914565