Calculus of Variations and Geometric Measure Theory

G. Barles - A. Briani - E. Chasseigne

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

created by briani on 12 Sep 2013
modified on 27 May 2014


Published Paper

Inserted: 12 sep 2013
Last Updated: 27 may 2014

Journal: SIAM Journal on Control and Optimization
Volume: 52
Number: 3
Pages: 1712-1744
Year: 2014
Doi: 10.1137/130922288
Links: HAL


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.

Keywords: optimal control, Viscosity solutions, Bellman Equation, discontinuous dynamics