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 in:SIAM journal on control and optimization Vol. 52; no. 5; pp. 2944 - 2969
Main Authors: Korda, Milan, Henrion, Didier, Jones, Colin N.
Format: Journal Article
Language:English
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
ISSN:0363-0129, 1095-7138
Online Access:Get full text
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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