Hybrid variables-dependent event-triggered model predictive control subject to polytopic uncertainties

Abstract

This paper focuses on the model predictive control (MPC) issue where the measurable state is released under an event-triggered mechanism (ETM) to implement MPC over an infinite horizon. A new dynamic ETM (DETM) is devised to conserve network resources, which contains an additive internal dynamic variable (IDV), a multiplicative adaptively adjusting variable, a time-varying weighting matrix and several flexible scalars. The MPC problem is formulated as a ‘min–max’ optimisation problem (OP), where a hard constraint and robust positive invariant set on the predictive state/IDV are considered simultaneously. By resorting to a Lyapunov-like function that depends on the IDV, we put forward an auxiliary OP with matrix-inequality-based constraints. By the feasible solutions of such an auxiliary OP, the feedback gain matrix is designed which ensures the asymptotic stability of the closed-loop system. Two examples are presented to demonstrate the validity of the devised DETM and the DETM-based MPC algorithm. The study verifies that the devised DETM has advantages over an existing counterpart in conserving network resources while achieving the desired performance.

Keywords:

• Model predictive control
• dynamic event-triggered mechanism
• hybrid variables
• networked control systems
• polytopic uncertainties

Disclosure statement

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

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant numbers 62073303 and 61673356], the Hubei Provincial Natural Science Foundation of China [grant number 2015CFA010], and the 111 Project of China [grant number B17040].

Notes on contributors

Xiongbo Wan

Xiongbo Wan received the B.S. degree in information and computing science in 2006 from Huazhong Agricultural University, Wuhan, China, the M.S. degree in probability theory and mathematical statistics in 2008 and the Ph.D. degree in control theory and engineering in 2011, both from the Huazhong University of Science and Technology, Wuhan, China. From December 2012 to June 2013, he was a Visiting Scholar of the Akita Prefectural University, Akita, Japan. From July 2011 to December 2014, he was a Lecturer and then an Associate Professor with the College of Engineering, Huazhong Agricultural University, Wuhan, China. From December 2016 to November 2017, he was a Visiting Scholar with the Department of Computer Science, Brunel University London, U.K. Since January 2015, he has been an Associate Professor with the School of Automation, China University of Geosciences, Wuhan, China. His research interests include fault diagnosis, networked control systems, and genetic regulatory networks.

Fan Wei

Fan Wei received the B.S. degree in automation from Huazhong University of Science and Technology, Wuhan, China, in 2018. He is currently working toward the M.S. degree in control engineering with School of Automation, China University of Geosciences, Wuhan, China. His current research interests include model predictive control and networked control systems.

Chuan-Ke Zhang

Chuan-Ke Zhang received the B.S. degree in automation and the Ph.D. degree in control science and engineering from Central South University, Changsha, China, in 2007 and 2013, respectively. He was a Research Associate with the Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool, U.K., from 2014 to 2016. He is currently a Professor with the School of Automation, China University of Geosciences, Wuhan, China. His current research interests include time-delay systems and power systems.

Min Wu

Min Wu received the B.S. and M.S. degrees in engineering from Central South University, Changsha, China, in 1983 and 1986, respectively, and the Ph.D. degree in engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1999. He was a Faculty Member with the School of Information Science and Engineering, Central South University, from 1986 to 2014, and was promoted to a Professor in 1994. In 2014, he moved to the China University of Geosciences, Wuhan, China, where he is a Professor with the School of Automation. He was a Visiting Scholar with the Department of Electrical Engineering, Tohoku University, Sendai, Japan, from 1989 to 1990, and a Visiting Research Scholar with the Department of Control and Systems Engineering, Tokyo Institute of Technology, from 1996 to 1999. He was a Visiting Professor with the School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham, U.K., from 2001 to 2002. His current research interests include robust control, process control, and intelligent systems. Dr. Wu was a recipient of the IFAC Control Engineering Practice Prize Paper Award in 1999 (together with M. Nakano and J. She). He is a Fellow of IEEE and a Fellow of the Chinese Association of Automation (CAA Fellow).