Reachability and minimal times for state constrained nonlinear problems without any controllability assumption

Olivier Bokanowski 1 Nicolas Forcadel 2 Hasnaa Zidani 3, 4
4 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CNRS - Centre National de la Recherche Scientifique : UMR7641, X - École polytechnique, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : We consider a target problem for a nonlinear system under state constraints. We give a new continuous level-set approach for characterizing the optimal times and the backward-reachability sets. This approach leads to a characterization via a Hamilton-Jacobi equation, without assuming any controllability assumption. We also treat the case of time-dependent state constraints, as well as a target problem for a two-player game with state constraints. Our method gives a good framework for numerical approximations, and some numerical illustrations are included in the paper.
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Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2010, 48 (7), pp. 4292-4316
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Dernière modification le : jeudi 12 avril 2018 - 01:48:13
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Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani. Reachability and minimal times for state constrained nonlinear problems without any controllability assumption. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2010, 48 (7), pp. 4292-4316. 〈hal-00395589〉

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