Junction conditions for finite horizon optimal control problems on multi-domains with continuous and discontinuous solutions

submitted
Publication type:
Paper in peer-reviewed journals
Keywords :
Hamilton-Jacobi equations; multi-domain control problems; value function;
Abstract:
This paper deals with junction conditions for Hamilton-Jacobi-Bellman (HJB) equations for finite horizon control problems on multi-domains. We consider two different cases where the final cost is continuous or lower semi-continuous. In the continuous case we extend the results in [26] in a more general framework with switching running costs and weaker controllability assumptions. The comparison principle has been established to guarantee the uniqueness and the stability results for the HJB system on such multi-domains. In the lower semi-continuous case, we characterize the value function as the unique lower semi-continuous viscosity solution of the HJB system, under a local controllability assumption.
BibTeX:
@article{Ghi-Rao-Zid-2200,
    author={Daria Ghilli and Zhiping Rao and Hasnaa Zidani },
    title={Junction conditions for finite horizon optimal control 
           problems on multi-domains with continuous and discontinuous 
           solutions },
    year={submitted },
}