Fuzzy-model-based ℋ_∞ filtering for discrete-time singular Markov jump nonlinear systems against hybrid attacks

Abstract

This paper investigates the ${\mathcal{H}}_{\mathrm{\infty }}$ filtering problem for a class of discrete-time singular Markov jump nonlinear systems against hybrid attacks via a fuzzy-model-based method, in which the hybrid attacks contain deception attacks and denial of service attacks. Two random variables subject to the Bernoulli distribution are used to describe whether the hybrid attacks are encountered during the measurement output of the original system being transmitted to the filter. By using linear matrix inequality technology and Lyapunov stability theory, some sufficient conditions are given to guarantee the considered systems are stochastically admissible and meet ${\mathcal{H}}_{\mathrm{\infty }}$ performance index γ. The design approach of the secure filter and a specific form to acquire the expected secure filter gains are obtained, respectively. Finally, to demonstrate the effectiveness of the proposed approach, both a numerical example and a practical example are provided.

Keywords:

• ${\mathcal{H}}_{\mathrm{\infty }}$ filtering
• fuzzy systems
• hybrid attacks
• singular Markov jump systems

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 under grant nos. [62273006,62173001,61873002,61703004]; The Major Natural Science Foundation of Higher Education Institutions of Anhui Province under grant no. [KJ2020ZD28]; Natural Science Foundation for Excellent Young Scholars of Anhui Province under grant no. [2108085Y21]; The Major Technologies Research and Development Special Program of Anhui Province under grant no. [202003a05020001]; The Key Research and Development Projects of Anhui Province under grant no. [202104a05020015]; The Open Project of China International Science and Technology Cooperation Base on Intelligent Equipment Manufacturing in Special Service Environment under grant no. [ISTC2021KF04]; The Anhui Provincial Natural Science Foundation under grant no. 2208085QF202; The Key Natural Science Foundation of Higher Education Institutions of Anhui Province under grant no. [KJ2021A0369]; The Open Fund of Anhui Engineering Laboratory for Intelligent Applications and Security of Industrial Internet under grant no. [IASII21-01].

Notes on contributors

Guanqi Wang

Guanqi Wang is now a M.S. candidate at the School of Electrical and Information Engineering, Anhui University of Technology, China. His current research interests include singular systems, Markov jump systems, networked control systems, fuzzy control, robust control and filtering.

Feng Li

Feng Li received the M.S. degree in Electrical Engineering from Anhui University of Technology, Ma'anshan, China, in 2017, and the Ph.D. degree in Control Science and Engineering from Nanjing University of Science and Technology, Nanjing, China, in 2021. He is currently a lecturer with the School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan, China. From April 2019 to November 2020, he was a visiting fellow with the School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, NSW, Australia. His current research interests include Markov jump systems, singularly perturbed systems, neural networks, networked control systems, robust control and filtering, and their applications.

Yan Wang

Yan Wang received the Ph.D. degree in Intelligent Monitoring and Control from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2008. She is currently a professor with the School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan China. From July 2014 to July 2015, she worked as a visiting scholar in Missouri University of Science and Technology, USA. Her current research interests include intelligent monitoring and control, structural health monitoring and modern control theory.

Jing Wang

Jing Wang received the Ph.D. degree in Electric Power System and Automation from Hohai University in 2019. She is currently an associate professor with the School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan, China. Her current research interests include Markov jump nonlinear systems, singularly perturbed systems, power systems, and nonlinear 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.