# Constructing robust feedback laws by set oriented numerical methods

L. Grüne, O. Junge:
**Constructing robust feedback laws by set oriented numerical methods**

in:
*Proceedings of the GAMM Annual Meeting,*
*
*
Luxembourg,
2005,
157 - 162

DOI:
10.1002/pamm.200510059

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## Abstract:

In two previous papers [Junge, Osinga 04; Grüne, Junge 05] a numerical method for the construction of optimally stabilizing feedback laws was proposed. The method is based on a set oriented discretization of phase space in combination with graph theoretic algorithms for the computation of shortest paths in directed weighted graphs. The resulting approximate optimal value function is piecewise constant, yielding an approximate optimal feedback which might not be robust with respect to perturbations of the system. In this contribution we extend the approach to the case of perturbed control systems. Based on the concept of a multivalued game we show how to derive a directed weighted hypergraph from the original system and generalize the corresponding shortest path algorithm. The resulting optimal value function yields a robustly stabilizing approximate optimal feedback law. This note is an abbreviated version of [Grüne, Junge 05a]. For the proofs of the statements here we refer to the full paper.