Characterization of the value function of final state constrained control problems with BV trajectories

Ariela Briani 1, 2 Hasnaa Zidani 2, 3
1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 UMA - Unité de Mathématiques Appliquées
3 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 : This paper aims to investigate a control problem governed by differential equations with Radon measure as data and with final state constraints. By using a known reparametrization method (by Dal Maso and Rampazzo [18]), we obtain that the value function can be characterized by means of an auxiliary control problem of absolutely continuous trajectories, involving time-measurable Hamiltonian. We study the characterization of the value function of this auxiliary problem and discuss its numerical approximations.
Keywords : Optimal control problem differential systems with measures as data measurable functions Hamilton-Jacobi equations sadco
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Communications on Pure and Applied Mathematics, Wiley, 2011, 10 (6), pp.1567-1587. 〈10.3934/cpaa.2011.10.1567〉
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Ariela Briani, Hasnaa Zidani. Characterization of the value function of final state constrained control problems with BV trajectories. Communications on Pure and Applied Mathematics, Wiley, 2011, 10 (6), pp.1567-1587. 〈10.3934/cpaa.2011.10.1567〉. 〈inria-00627518〉

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