Relaxation for a Class of Control Systems with Unilateral Constraints

Abstract

We consider a nonlinear control system involving a maximal monotone map and with a priori feedback. We assume that the control constraint multifunction U(t, x) is nonconvex valued and only lsc in the x∈ RN variable. Using the Q-regularization (in the sense of Cesari) of U(t, ⋅ ) , we introduce a relaxed system. We show that this relaxation process is admissible.