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

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 :
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

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

### Fichiers

MultiDomain-SIAM-revised.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : hal-00825778, version 2
• ARXIV : 1305.5813

### Citation

Guy Barles, Ariela Briani, Emmanuel Chasseigne. A Bellman approach for regional optimal control problems in $\R^N$. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (3), pp.1712-1744. 〈hal-00825778v2〉

### Métriques

Consultations de la notice

## 406

Téléchargements de fichiers