Doria Affane - LMPA Laboratory, Department of Mathematics, Jijel University, PB۹۸, Cite Ouled Aissa, Jijel, Algeria
Mustapha Fateh Yarou - LMPA Laboratory, Department of Mathematics, Jijel University, PB۹۸, Cite Ouled Aissa, Jijel, Algeria

This paper deals with nonconvex set-valued perturbation to second order nonlinear evolution system governed by the so-called nonconvex sweeping process for a class of subsmooth moving sets depending on state and velocity. Making use of our recent paper obtained for a convex valued perturbation, we prove a new existence result when the perturbations are \textit{almost convex}. Furthermore, we apply our result in the study of an optimal control problem known as a \textit{minimum time problem}.

Sweeping process, subsmooth sets, almost convex, attainable set, minimum time problem