General second order functional differential inclusion driven by the sweeping process with subsmooth sets

Abstract

In this paper, we consider a perturbed second order nonconvex sweeping process for a class of subsmooth moving sets depending jointly on time, state and velocity. The perturbation, known as the external forces applied on the system, is general and takes the form of a sum of a single-valued continuous mapping and a set-valued unbounded mapping. We generalize earlier results obtained for this kind of problems. We deal also with a delayed perturbation, we extend a discretization approach known for the time-dependent sweeping process to the case when the moving set depends also on state and velocity.