# 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.
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https://hal.archives-ouvertes.fr/hal-00825778
Contributor : Guy Barles <>
Submitted on : Friday, January 24, 2014 - 2:07:06 PM
Last modification on : Friday, October 25, 2019 - 12:18:19 PM
Document(s) archivé(s) le : Thursday, April 24, 2014 - 10:45:56 PM

### Files

MultiDomain-SIAM-revised.pdf
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### Identifiers

• 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⟩

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