On output regulation in systems with differential variational inequalities

We consider the problem of designing state feedback control laws for output regulation in a class of dynamical systems which are described by variational inequalities and ordinary differential equations. In our setup, these variational inequalities are used to model state trajectories constrained to evolve within time-varying, closed, and convex sets, and systems with complementarity relations. We first derive conditions to study the existence and uniqueness of solutions in such systems. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available; In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed.