Event-triggered H_–/L_∞ fault detection observer design for discrete-time Lipschitz nonlinear networked control systems in finite-frequency domain

Abstract

This paper proposes an event-triggered $H_{-}/L_{\mathrm{\infty }}$ fault detection observer (FDO) design method for discrete-time Lipschitz nonlinear networked control systems (NCSs) in finite-frequency domain. First, a discrete event-triggered transmission scheme is proposed to mitigate the utility of limited network bandwidth. Second, with the aid of a reformulated Lipschitz property, the nonlinear error dynamics are converted into a linear parameter varying (LPV) networked system model. Third, based on this model, the finite-frequency $H_{\mathrm{\_}}/L_{\mathrm{\infty }}$ index is used to measure the worst-case fault sensitivity performance and the $H_{\mathrm{\_}}$ norm from unknown disturbance to residual is used to measure disturbance robustness performance. Next, a residual evaluation and a dynamic threshold are synthesised based on the $L_{\mathrm{\infty }}$ norm. Furthermore, sufficient conditions of the FDO design are derived and transformed by a set of linear matrix inequalities (LMIs). The proposed FDO design method can significantly reduce the data transmission to relieve the communication pressure, and can also achieve better FD performance than the full frequency domain. Finally, A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

Keywords:

• Networked control systems
• linear matrix inequalities
• Lipschitz nonlinear systems
• $L_{\mathrm{\infty }}$ fault detection observer
• event-triggered scheme
• finite frequency

Disclosure statement

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

Additional information

Funding

This work was partly supported by the National Natural Science Foundation of China [grant number 61503184].

Notes on contributors

Yanping Wang

Yanping Wang received the B.S. degree in Electrical Engineering and Intelligent Control from Soochow University, China, in 2018. Currently, she is pursuing the M.S. degree in Control Theory and Control Engineering from Nanjing University of Aeronautics and Astronautics, China. Her research interests include fault detection, nonlinear systems and networked control systems.

Xiaoming Chen

Xiaoming Chen received the B.S. degree in Automation from Qufu Normal University in 2008. She obtained the M.S. degree in Control Science and Engineering from Harbin Institute of Technology in 2010, and she joined Nanjing University of Aeronautics and Astronautics, in 2014, taking an associate professor in College of Automation Engineering. Her research interests include positive systems, fuzzy systems, delay systems, 2-D systems, estimation and filtering, stochastic control and robust control.

Haixiao Guo

Haixiao Guo received the B.S. degree in Detection, Guidance and Control Technology from Nanjing University of Aeronautics and Astronautics, China, in 2018. Currently, he is pursuing the M.S.degree in Control Engineering from Nanjing University of Aeronautics and Astronautics, China. His research interests include fault detection, interconnected systems and networked control systems.