(Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains

G Barles (1, 2) , Emmanuel Chasseigne (2, 1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 FDP - Fédération de recherche Denis Poisson

We revisit the pioneering work of Bressan & Hong on deterministic control problems in stratified domains, i.e. control problems for which the dynamic and the cost may have discontinuities on submanifolds of R N . By using slightly different methods, involving more partial differential equations arguments, we (i) slightly improve the assumptions on the dynamic and the cost; (ii) obtain a comparison result for general semi-continuous sub and supersolutions (without any continuity assumptions on the value function nor on the sub/supersolutions); (iii) provide a general framework in which a stability result holds.

Mots clés: viscosity solutions; Bellman Equation; Key-words: Optimal control; discontinuous dynamic

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

G Barles, Emmanuel Chasseigne. (Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains. 2015. ⟨hal-01097167v2⟩