Event-triggered stabilisation of switched nonlinear systems with actuator saturation: a Hamiltonian approach

ABSTRACT

This paper presents a Hamiltonian approach to study the event-triggered stabilisation problem of switched affine nonlinear systems with actuator saturation. The key idea is to obtain an event-triggered control strategy by developing a constant Hamiltonian realisation method, an average dwell time (ADT) scheme and a nonlinear sector method. The proposed strategy can ensure the asymptotic stability of the plant without violating actuator saturation, even if there exists asynchronous phenomenon between the subsystems and their candidate controllers. The results presented in this paper remove the common assumption that the system's mode and controller's mode have to be synchronised and that the triggering condition has to be monitored continuously. This extends available results for switched nonlinear systems and reduces energy consumptions. Finally, an example is provided to verify the validity of the proposed results.

KEYWORDS:

• Switched affine nonlinear systems
• Hamiltonian approach
• event-triggered control
• actuator saturation
• mismatched behaviour

Disclosure statement

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

Data availability statement

All data generated or analysed during this study are included in this published article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant Nos. 62073189 and 62173207.

Notes on contributors

Qi Zhang

Qi Zhang received the B.S. degree in applied mathematics from the School of Mathematical Sciences, Liaocheng University, Liaocheng, China, in 2019. She is currently pursuing the M.S. degree with the Institute of Automation, Qufu Normal University, Qufu, China. Her research interests include nonlinear systems control, Hamiltonian systems and event-triggered control.

Weiwei Sun

Weiwei Sun received the B.Sc. degree in applied mathematics and the M.Sc. degree in control theory from Qufu Normal University, Qufu, China, in 2002 and 2005, respectively, and the Ph.D. degree in control theory and control engineering from Shandong University, Jinan, China, in 2009. She was a Visiting Scholar with the Department of Electrical and Computer Engineering, University of Virginia, VA, USA, from 2007 to 2008 and with the Department of Computer Science, Brunel University London, Uxbridge, U.K., in 2018. She is currently a Professor with the School of Engineering and the Institute of Automation, Qufu Normal University. She has published over 30 articles in refereed international journals. Her current research interests include nonlinear systems control, constrained system control and its application in wind power systems, and control and application of Hamiltonian systems in network environments.

Chaoqian Qiao

Chaoqian Qiao received the B.S. degree in Automation from the School of engineering institute, Qufu Normal University, Rizhao, China, in 2019. He is currently pursuing the M.S. degree with the Institute of Automation, Qufu Normal University, Qufu, China. Her research interests include permanent magnet synchronous motorPMSM) systems, Hamiltonian systems and robotic systems.