Secure control for discrete-time hidden Markov jump systems subject to replay attacks via output feedback

Abstract

This paper investigates the static output feedback secure control problem for discrete-time hidden Markov jump systems against replay attacks. The main purpose is to realise that closed-loop systems are stochastically stable with or without replay attacks. Firstly, the tampered sensors under replay attacks can be identified via the proposed detection method. Then, an asynchronous static output feedback controller is designed, which can eliminate the negative impact caused by replay attacks in view of the detection results. Based on the linear matrix inequality technique, some sufficient conditions which ensure the closed-loop systems are stochastically stable and meet a given $H_{\mathrm{\infty }}$ performance are established. Finally, a numerical example and a practical example are given to verify the effectiveness and superiority of the proposed method.

Keywords:

• Hidden Markov jump systems
• static output feedback control
• replay attacks
• $H_{\mathrm{\infty }}$ performance

Disclosure statement

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

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 62103005], the Major Natural Science Foundation of Higher Education Institutions of Anhui Province [grant number KJ2020ZD28], the Major Technologies Research and Development Special Program of Anhui Province under Grant 202003a05020001, the Natural Science Foundation of Anhui Provincial Natural Science Foundation [grant number 2108085QF276], the Key research and development projects of Anhui Province [grant number 202104a05020015], the Opening Project of Key Laboratory of Power Electronics and Motion Control of Anhui Higher Education Institutions [grant number OP14100135].

Notes on contributors

Lei Su

Lei Su received the M.S. degree in the School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan, China, in 2016 and the Ph.D. degree in control theory and engineering from the Northeastern University in 2020. Now, he is a lecturer at the School of Electrical and Information Engineering, Anhui University of Technology, China. His research interests include fault-tolerant control, event-triggered control, Markov jump systems and cyber-physical systems.

Shinian Fang

Shinian Fang graduated from Northeast University in June 1987, majoring in material processing and control, and worked in Huatian Engineering and Technology Corporation, MCC as a senior engineer. Engaged in research on intelligent processing control.

Zijun Liu

Zijun Liu received the B.Sc. degree in Automation from Hubei University of Arts and Science, Xiangyang, China, in 2019 and the M.S. degree in the School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan, China, in 2021. Now he works in Huatian Engineering and Technology Corporation, MCC as a primary engineer. Engaged in research on intelligent processing control.

Hao Shen

Hao Shen received the Ph.D. degree in control theory and control engineering from Nanjing University of Science and Technology, Nanjing, China, in 2011. Since 2011, he has been with Anhui University of Technology, China, where he is currently a Professor. His current research interests include stochastic hybrid systems, complex networks, fuzzy systems and control, nonlinear control. Dr Shen has served on the technical program committee for several international conferences. He is an Associate Editor/Guest Editor for several international journals, including Journal of The Franklin Institute, Applied Mathematics and Computation, Neural Processing Letters and Transactions of the Institute Measurement and Control. Prof. Shen was a recipient of the Highly Cited Researcher Award by Clarivate Analytics (formerly, Thomson Reuters) in 2019–2021.

Tian Fang

Tian Fang graduated from University of Science and Technology Beijing, majoring in control theory and control engineering, and worked in Huatian Engineering and Technology Corporation, MCC as a senior engineer. Engaged in research on control theory and intelligent control.