On the solution existence for prox-regular perturbed sweeping processes

Abstract

In the setting adopted by Edmond and Thibault [Relaxation of an optimal control problem involving a perturbed sweeping process, Math. Program. 104 (2005), 347-373], we study a class of perturbed sweeping processes. Under suitable assumptions, we obtain two solution existence theorems for the perturbed sweeping processes with the constraint sets being prox-regular sublevel sets. The results are applied to the behavior of some concrete mechanical sweeping processes, which appear for the first time in this paper.