Topological properties for a perturbed first order sweeping process

• Main Authors: Affane Doria, Boulkemh Loubna
• Format: Article
• Language: English
• Published: Sciendo 2021-08-01
• Series: Acta Universitatis Sapientiae: Mathematica
• Subjects: sweeping process; subsmooth sets; perturbation; almost convex; attainable sets; time optimal control problems; 34a60; 28a25
• Online Access: https://doi.org/10.2478/ausm-2021-0001

In this paper, we consider a perturbed sweeping process for a class of subsmooth moving sets. The perturbation is general and takes the form of a sum of a single-valued mapping and a set-valued mapping. In the first result, we study some topological proprieties of the attainable set, the set-valued mapping considered here is upper semi-continuous with convex values. In the second result, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity. Then, we deduce a solution of the time optimality problem.