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| HAL: hal-00415953, version 1 |
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| Available versions: | v1 (2009-09-11) |
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| Deterministic state constrained optimal control problems without controllability assumptions |
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| Olivier Bokanowski 1Nicolas Forcadel 2 |
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| (2009-09-11) |
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| In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position $x$. In the constrained case, when no controllability assumption is made, the HJB equation may have several solutions. Our first result aims to give the precise information that should be added to the HJB equation in order to obtain a characterization of the value function. This result is very general and holds even when the dynamics is not continuous and the state constraints set is not smooth. On the other hand we study also some stability results for relaxed or penalized control problems. |
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| 1: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| 2: | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| 3: | Commands (INRIA Futurs) |
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INRIA – CNRS : UMR7641 |
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| 4: | École Nationale Supérieure de Techniques Avancées (ENSTA ParisTech) |
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ENSTA ParisTech |
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| Subject | : | Mathematics/Analysis of PDEs Mathematics/Numerical Analysis |
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| Optimal control problem – state constraints – Hamilton-Jacobi equation. |
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| hal-00415953, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00415953 | |
| oai:hal.archives-ouvertes.fr:hal-00415953 | |
| From: Nicolas Forcadel | |
| Submitted on: Friday, 11 September 2009 15:07:06 | |
| Updated on: Friday, 11 September 2009 15:32:46 | |
