Junction conditions for finite horizon optimal control problems on multi-domains with continuous and discontinuous solutions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 79.

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 Z. Rao and H. Zidani, Hamilton-Jacobi-Bellman equations on multi-domains, in Control and Optimization with PDE Constraints, Vol. 164 of International Series of Numerical Mathematics. Birkhäuser, Basel (2013) 93–116. 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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018072
Classification : 49L20, 49J15, 35F21
Mots-clés : Optimal control, Hamilton–Jacobi–Bellman equations, multi-domains, junction conditions
Ghilli, Daria 1 ; Rao, Zhiping 1 ; Zidani, Hasnaa 1

1 
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Ghilli, Daria; Rao, Zhiping; Zidani, Hasnaa. Junction conditions for finite horizon optimal control problems on multi-domains with continuous and discontinuous solutions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 79. doi : 10.1051/cocv/2018072. http://archive.numdam.org/articles/10.1051/cocv/2018072/

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