On the Solution Existence for Prox-Regular Perturbed Sweeping Processes

TL;DR

This paper establishes the existence of solutions for a class of perturbed sweeping processes with prox-regular constraints and applies these results to analyze specific mechanical sweeping systems.

Contribution

It provides the first analysis of certain mechanical sweeping processes using solution existence theorems for perturbed sweeping processes with prox-regular sets.

Findings

Existence theorems for solutions under specific conditions

Application to concrete mechanical sweeping processes

First-time analysis of these mechanical systems

Abstract

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