Convex computation of the maximum controlled invariant set for discrete-time polynomial control systems
- 1 December 2013
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE) in 52nd IEEE Conference on Decision and Control
- p. 7107-7112
- https://doi.org/10.1109/cdc.2013.6761016
Abstract
We characterize the maximum controlled invariant (MCI) set for discrete-time systems as the solution of an infinite-dimensional linear programming problem. In the case of systems with polynomial dynamics and semialgebraic state and control constraints, we describe a hierarchy of finite-dimensional linear matrix inequality relaxations of this problem that provides outer approximations with guaranteed set-wise convergence to the MCI set. The approach is compact 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.Keywords
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