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 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.


Published in:
Siam Journal on Control and Optimization, accepted, 52, 5, 2944-2969
Year:
2014
Publisher:
Philadelphia, Society for Industrial and Applied Mathematics
Keywords:
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 Record created 2014-07-08, last modified 2018-03-17

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