A Bellman approach for regional optimal control problems in $\R^N$

Guy Barles; Ariela Briani; Emmanuel Chasseigne

A Bellman approach for regional optimal control problems in $\R^N$

Guy Barles ^{1, 2} Ariela Briani ^{1, 2} Emmanuel Chasseigne ^{1, 2}

1 FDP - Fédération de recherche Denis Poisson

2 LMPT - Laboratoire de Mathématiques et Physique Théorique

Abstract : This article is a continuation of a previous work where we studied infinite horizon control problems for which the dynamic, running cost and control space may be different in two half-spaces of some euclidian space $\R^N$. In this article we extend our results in several directions: $(i)$ to more general domains; $(ii)$ by considering finite horizon control problems; $(iii)$ by weaken the controlability assumptions. We use a Bellman approach and our main results are to identify the right Hamilton-Jacobi-Bellman Equation (and in particular the right conditions to be put on the interfaces separating the regions where the dynamic and running cost are different) and to provide the maximal and minimal solutions, as well as conditions for uniqueness. We also provide stability results for such equations.

keyword : viscosity solutions Optimal control discontinuous dynamic Bellman Equation viscosity solutions.

Type de document :

Article dans une revue

SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (3), pp.1712-1744

Domaine :

Mathématiques [math] / Equations aux dérivées partielles [math.AP]

Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00825778
Contributeur : Guy Barles <>
Soumis le : vendredi 24 janvier 2014 - 14:07:06
Dernière modification le : jeudi 7 février 2019 - 14:28:18
Document(s) archivé(s) le : jeudi 24 avril 2014 - 22:45:56

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A Bellman approach for regional optimal control problems in $\R^N$

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