On nonconvex differential inclusions whose state is constrained in the closure of an open set. Applications to dynamic programming

Abstract

Results of the type of Filippov's Theorem are proved for nonconvex differential inclusions whose state variable is constrained in the closure of an open subset of $\mathbb{R}^n$. An application is provided to dynamic programming for optimal control problems with state constraints and a control set depending on the time and the state.