Hamilton–Jacobi–Bellman Approach for Optimal Control Problems of Sweeping Processes

Abstract

This paper is concerned with a state constrained optimal control problem governed by a Moreau’s sweeping process with a controlled drift. The focus of this work is on the Bellman approach for an infinite horizon problem. In particular, we focus on the regularity of the value function and on the Hamilton–Jacobi–Bellman equation it satisfies. We discuss a uniqueness result and we make a comparison with standard state constrained optimal control problems to highlight a regularizing effect that the sweeping process induces on the value function.