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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Veröffentlicht in:	SIAM journal on control and optimization Jg. 52; H. 5; S. 2944 - 2969
Hauptverfasser:	Korda, Milan, Henrion, Didier, Jones, Colin N.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Society for Industrial and Applied Mathematics 01.01.2014
Schlagworte:	Approximation Control systems Dynamical systems Hierarchies Invariants Mathematics Nonlinear dynamics Optimization Optimization and Control Polynomials
ISSN:	0363-0129, 1095-7138
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Abstract	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.
AbstractList	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.
Author	Korda, Milan Henrion, Didier Jones, Colin N.
Author_xml	– sequence: 1 givenname: Milan surname: Korda fullname: Korda, Milan – sequence: 2 givenname: Didier surname: Henrion fullname: Henrion, Didier – sequence: 3 givenname: Colin N. surname: Jones fullname: Jones, Colin N.
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Snippet	We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an...
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SubjectTerms	Approximation Control systems Dynamical systems Hierarchies Invariants Mathematics Nonlinear dynamics Optimization Optimization and Control Polynomials
Title	Convex Computation of the Maximum Controlled Invariant Set For Polynomial Control Systems
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