On a controllability problem for a feedback control system governed by a semilinear differential equation and a sweeping process

Abstract

We consider a controllability problem for a feedback control system governed by a semilinear differential equation and a sweeping process in Hilbert spaces. We define the operator whose fixed points are generating solutions of the problem. By applying the methods of the fixed point theory for condensing maps we study the properties of this operator, in particular, we prove that under certain conditions it is condensing w.r.t. an appropriate measure of noncompactness. This allows to present the general controllability principle.