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Numerical Schemes for Discontinuous Value Functions of Optimal Control |
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| Authors: | Pierre Cardaliaguet Marc Quincampoix Patrick Saint-Pierre |
| Affiliation: | (1) Centre de Recherche Viabilité, Jeux, Contrôle - CNRS E.R.S. 2064, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775 Paris cedex 16, France;(2) Département de Mathématiques, Faculté des Sciences et Techniques, Université de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, BP 809, 29285 Brest, France |
| Abstract: | In this paper we explain that various (possibly discontinuous) value functions for optimal control problem under state-constraints can be approached by a sequence of value functions for suitable discretized systems. The key-point of this approach is the characterization of epigraphs of the value functions as suitable viability kernels. We provide new results for estimation of the convergence rate of numerical schemes and discuss conditions for the convergence of discrete optimal controls to the optimal control for the initial problem. |
| Keywords: | viability optimal control value function |
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