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.

Keywords:

• Output feedback
• robust control
• constraints
• invariant sets
• set-membership observer

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author, C. E. T. Dórea, upon reasonable request.

Additional information

Funding

This work was partially supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil, grant # 309862/2019-1.

Notes on contributors

J. I. S. Silveira Júnior

J. I. S. Silveira Júnior received the B.Sc. degree in Computer Engineering and M.Sc. Degree in Electrical and Computer Engineering from the Universidade Federal do Rio Grande do Norte, Natal, Brazil, in 2013 and 2016, respectively. Since 2011, he has been working as a Computer Technician and Researcher at the Universidade Federal do Rio Grande do Norte. He is presently a candidate for the Ph.D. degree in Electrical and Computer Engineering at the Universidade Federal do Rio Grande do Norte. His current research interests include uncertain linear systems, robust control, invariant sets, and their applications.

C. E. T. Dórea

C. E. T. Dórea received the B.Sc. degree in Electrical Engineering from the Universidade Federal da Bahia, Brazil, in 1990, the M.Sc. degree in Electrical Engineering from UNICAMP, Brazil, in 1993, and the D.Sc. degree in Control Systems from Université Paul Sabatier, France, in 1997. Since 2010, he has been with the Department of Computer Engineering and Automation at the Universidade Federal do Rio Grande do Norte, Brazil, where he is now a full Professor. His main research interests include linear systems theory and design, set-invariance techniques for control and state estimation under constraints, optimisation-based control design and predictive control applications.