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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

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00812846
Date
2014
Journal name
SIAM Journal on Control and Optimization
Volume
52
Number
5
Publisher
SIAM
Pages
2917–2943
Publication identifier
http://dx.doi.org/10.1137/130916709
Metadata
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Author(s)
Rao, Zhiping
Forcadel, Nicolas cc
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 / Keywords
multi-domains; essential Hamiltonians; Hamilton-Jacobi-Bellman equations; optimal control; singular perturbations

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