On output regulation in systems with differential variational inequalities

Abstract

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. 53rd IEEE Conference on Decision and Control

Differential-algebraic inclusions with maximal monotone operators

“…Proof: Once we have arrived at (15) in Lemma 3, then we can apply transformations (20) and (19) follows readily. By construction, P is positive semidefinite, and it only remains to show that M is maximal monotone.…”

“…Another instance of such DIs is observed in differential variational inequalities [10] which appear in the solutions of the optimal control problems. More recently, the control design problems for such systems has also attracted a lot of attention [14], [15]. The study of DAIs (1) is thus aimed at enlarging the class of systems treated in aforementioned references, and finding applications which cannot be treated within the existing frameworks.…”

Output Regulation in Differential Variational Inequalities using Internal Model Principle and Passivity‐Based Approach

“…Using the certainty equivalence principle, the compensator first estimates the state variables x(·) and x r (·) and then defines the control law as a function of these estimates. For details, see [8].…”

“…From control perspective, DVIs form an important class of nonsmooth dynamical systems and lately several controltheoretic problems have been studied for such systems [6][7][8]. The problem of output regulation relates to designing control laws for asymptotically tracking a reference trajectory or rejecting disturbances.…”

“…The problem of output regulation for a simpler class of DVIs was introduced in our work [7,8] and in this paper, we present a summary of results for a more generalized system class based on the recent research work. While VIs can also be written using the notion of (set-valued) normal cone operators so that the differential inclusion resulting from (1) has maximal monotone operators, the introduction of matrices G, H, J and the vector field f (·, ·) may not preserve monotonicity which makes it difficult to study the solution of such systems.…”