Singular perturbation of optimal control problems on multi-domains

Nicolas Forcadel 1, 2 Zhiping Rao 2, 3
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, Univ. Paris-Saclay, ENSTA ParisTech - École Nationale Supérieure de Techniques Avancées, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : The goal of this paper is to study a singular perturbation problem in the framework of optimal control on multi-domains. We consider an optimal control problem in which the controlled system contains a fast and a slow variables. This problem is reformulated as an Hamilton-Jacobi-Bellman (HJB) equation. The main difficulty comes from the fact that the fast variable lives in a multi-domain. The geometric singularity of the multi-domains leads to the discontinuity of the Hamiltonian. Under a controllability assumption on the fast variables, the limit equation (as the velocity of the fast variable goes to infinity) is obtained via a PDE approache and by means of the tools of the control theory.
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Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (5), pp.2917-2943. <10.1137/130916709>
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Nicolas Forcadel, Zhiping Rao. Singular perturbation of optimal control problems on multi-domains. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (5), pp.2917-2943. <10.1137/130916709>. <hal-00812846>

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