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

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 ge...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2014, Vol.52 (3)
Main Authors: Barles, Guy, Briani, Ariela, Chasseigne, Emmanuel
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
Online Access:Get full text
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Summary: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.
ISSN:0363-0129
1095-7138
DOI:10.1137/130922288