Homogenization Results for a Deterministic Multi-domains Periodic Control Problem

Guy Barles (1, 2) , Ariela Briani (1, 2) , Emmanuel Chasseigne (1, 2) , Nicoletta Tchou (3)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 FDP - Fédération de recherche Denis Poisson
3 IRMAR - Institut de Recherche Mathématique de Rennes

We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control problems, the three first authors have shown that several value functions can be defined, depending, in particular, of the choice is to use only ''regular strategies'' or to use also ''singular strategies''. We study the homogenization problem in these two different cases. It is worth pointing out that, if the second one can be handled by usual partial differential equations method " á la Lions-Papanicolaou-Varadhan" with suitable adaptations, the first case has to be treated by control methods (dynamic programming).

Mots clés: viscosity solutions; Homogenization; deterministic optimal control; discontinuous dynamic; cell problem; Bellman Equation; viscosity solutions.

Domaines: Equations aux dérivées partielles [math.AP]

Guy Barles, Ariela Briani, Emmanuel Chasseigne, Nicoletta Tchou. Homogenization Results for a Deterministic Multi-domains Periodic Control Problem. Asymptotic Analysis, 2015, 95 (3-4), pp.243-278. ⟨10.3233/ASY-151322⟩. ⟨hal-00986700⟩