Reference tracking via output feedback for constrained uncertain linear systems

Abstract

In this paper we propose a robust output feedback control scheme for constant reference tracking in uncertain linear systems subject to state and control constraints. First, we establish conditions under which a polyhedral set is Output Feedback Controlled Invariant with respect to a linear system subject to polytopic uncertainties, i.e. a set guaranteeing robust constraint satisfaction via output feedback. Then, we build a dynamic output feedback controller for the uncertain model based on set-membership observers, allowing the reduction of the set of possible states consistent with the measurements. Finally, to reduce the tracking error, we propose a model update procedure that adjusts the nominal model used for tracking to the output measurements. Numerical experiments illustrate the ability of the proposed controller to achieve reference tracking with reduced offset for the uncertain systems under consideration. To the best of our knowledge, it is one of the first works that addresses constant reference tracking in uncertain linear systems under constraints with output feedback.