Convex computation of the maximum controlled invariant set for polynomial control systems
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.
Cite
@article{arxiv.1303.6469,
title = {Convex computation of the maximum controlled invariant set for polynomial control systems},
author = {Milan Korda and Didier Henrion and Colin N. Jones},
journal= {arXiv preprint arXiv:1303.6469},
year = {2013}
}