Singular perturbation of optimal control problems on multi-domains
Rao, Zhiping; Forcadel, Nicolas (2014), Singular perturbation of optimal control problems on multi-domains, SIAM Journal on Control and Optimization, 52, 5, p. 2917–2943. http://dx.doi.org/10.1137/130916709
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00812846
Journal nameSIAM Journal on Control and Optimization
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Abstract (EN)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.
Subjects / Keywordsmulti-domains; essential Hamiltonians; Hamilton-Jacobi-Bellman equations; optimal control; singular perturbations
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