On the solution existence for prox-regular perturbed sweeping processes
Journal of Nonlinear and Variational Analysis · 2021
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.