<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Topological properties for a perturbed first order sweeping process

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Topological properties for a perturbed first order sweeping process"}

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...

Topological properties for a perturbed first order sweeping process

Published Online: Aug 26, 2021

Page range: 1 - 22

Received: Dec 25, 2020

DOI: https://doi.org/10.2478/ausm-2021-0001

Keywords
sweeping process, subsmooth sets, perturbation, almost convex, attainable sets, time optimal control problems

© 2021 Doria Affane et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Topological properties for a perturbed first order sweeping process

Published Online: Aug 26, 2021

Page range: 1 - 22

Received: Dec 25, 2020

DOI: https://doi.org/10.2478/ausm-2021-0001

Keywordssweeping process, subsmooth sets, perturbation, almost convex, attainable sets, time optimal control problems

© 2021 Doria Affane et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
sweeping process, subsmooth sets, perturbation, almost convex, attainable sets, time optimal control problems