Event-triggered control for discrete-time systems with unknown nonlinearities: an interval observer-based approach

Abstract

This paper is concerned with the interval observer-based control for a class of nonlinear systems with unknown nonlinearities. For the purpose of effectively reducing network congestion and improving resource utilisation, an event-triggered strategy is proposed for the channel between the interval observer and the controller. The designed controller with two gains is nontrivial and adequately utilises the real-time information of both the upper bound and the lower bound of system states. By using the monotonicity theory combined with the Lyapunov stability, some sufficient conditions are developed to ensure the closed-loop system with the given event-triggering scheme is input-to-state stable with the simultaneous presence of external disturbances and unknown nonlinearities. Two controller gain matrices and an observer gain are designed via the solution of a set of matrix inequalities. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Keywords:

• Interval observer
• non-linear systems
• event-triggered scheme
• input-to-state stability (ISS)
• monotonicity theory

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant No. 61873169 and 61973219, the Natural Science Foundation of Shanghai [grant number 18ZR1427000], the China Postdoctoral Science Foundation [grant number 2019TQ0202], and the Shanghai Pujiang Program [grant number 19PJ1408100].

Notes on contributors

Guoliang Wei

Guoliang Wei received the B.Sc. degree in mathematics from Henan Normal University, Xinxiang, China, in 1997 and the M.Sc. degree in applied mathematics and the Ph.D. degree in control engineering, both from Donghua University, Shanghai, China, in 2005 and 2008, respectively. He is currently a Professor with the College of Science, University of Shanghai for Science and Technology, Shanghai. From 2010 to 2011, he was an Alexander von Humboldt Research Fellow with the Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg, Germany. From 2009 to 2010, he was a Post-Doctoral Research Fellow with the Department of Information Systems and Computing, Brunel University London, Uxbridge, U.K., sponsored by the Leverhulme Trust of the U.K. He was a Research Assistant with the University of Hong Kong, Hong Kong, for two months, in 2007 and with the City University of Hong Kong, Hong Kong, for two months, in 2008. He has published over 50 papers in refereed international journals. His current research interests include nonlinear systems, stochastic systems, and bioinformatics. Dr. Wei is a very active reviewer for many international journals.

Linlin Liu

Linlin Liu received the B.Sc. degree in mathematics from Luoyang Normal University, Luoyang, China, in 2017. She is currently pursuing the M.Sc. degree from College of Science, University of Shanghai for Science and Technology, Shanghai, China. Her current research interests include nonlinear systems, event-triggered control, networked dynamical systems, control theory and applications.

Licheng Wang

Licheng Wang received the B.Sc. degree in automation from Weifang University, Weifang, China, in 2011 and the M.Sc. degree in control science and engineering from the University of Shanghai for Science and Technology, Shanghai, China, in 2014, where he is currently pursuing the Ph.D. degree. Since 2016, he has been a visiting Ph.D. student with the Department of Electronic and Computer Engineering, Brunel University London, Uxbridge, U.K. His current research interests include nonlinear stochastic control and filtering, as well as complex network and sensor networks. Mr. Wang is currently a reviewer for some international journals.

Derui Ding

Derui Ding received both the B.Sc. degree in Industry Engineering in 2004 and the M.Sc. degree in Detection Technology and Automation Equipment in 2007 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in Control Theory and Control Engineering in 2014 from Donghua University, Shanghai, China. From July 2007 to December 2014, he was a teaching assistant and then a lecturer in the Department of Mathematics, Anhui Polytechnic University, Wuhu, China. He is currently a senior research fellow with the School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, Australia. From June 2012 to September 2012, he was a research assistant in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong. From March 2013 to March 2014, he was a visiting scholar in the Department of Information Systems and Computing, Brunel University London, UK. His research interests include nonlinear stochastic control and filtering, as well as multi-agent systems and sensor networks. He has published around 40 papers in refereed international journals. Dr. Ding is serving as an Associate Editor for Neurocomputing. He is also a very active reviewer for many international journals.