Stability analysis of networked control systems under DoS attacks in frequency domain via game theory strategy

Abstract

In this paper, the stability analysis of networked control systems (NCSs) under Denial-of-Service (DoS) attacks is studied. Firstly, the stability analysis for NCSs free of DoS attacks is investigated. Considering the DoS attacks, the game theory is introduced to establish the non-cooperative game between defender and attacker of NCSs. At the same time, the stability of NCSs is analysed in frequency domain, and the signal-to-noise ratio (SNR) expression is given by using spectral decomposition technique and Nash equilibrium (NE) strategy. The packet dropout phenomenon caused by DoS attacks is described by Bernoulli distribution. By virtue of the NE strategy, the stability of NCSs can be optimised. In the obtained results, the influence of the traditional constraints and DoS attacks is illustrated. Finally, some numerical examples are given to show the effectiveness of the derived theoretical results.

Keywords:

• Denial-of-Service (DoS) attacks
• nash equilibrium (NE) strategy
• networked control systems (NCSs)
• non-cooperative game
• stability analysis

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant This work is supported by National Natural Science Foundation of China (62073143, 61922063, 62072164), Program of Shanghai Academic Research Leader (19XD1421000), Shanghai International Science and Technology Cooperation Project (18510711100), Shanghai and HongKong-Macao-Taiwan Science and Technology Cooperation Project (19510760200), Shanghai Shuguang Project (18SG18), and Innovation Program of Shanghai Municipal Education Commission (2021-01-07-00-02-E00107).

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant This work is supported by National Natural Science Foundation of China (62073143, 61922063), Program of Shanghai Academic Research Leader (19XD1421000), Shanghai International Science and Technology Cooperation Project (18510711100), Shanghai and HongKong-Macao-Taiwan Science and Technology Cooperation Project (19510760200), Shanghai Shuguang Project (18SG18), and Innovation Program of Shanghai Municipal Education Commission (2021-01-07-00-02-E00107).

Notes on contributors

Lingli Cheng

Lingli Cheng received the MS degree in College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi, China in 2018. She is currently pursuing the PhD degree with the School of Information Science and Engineering, East China University of Science and Technology, Shanghai,China. Her current research interests include net-work control systems, event-triggered mechanism and cyber attacks.

Huaicheng Yan

Huaicheng Yan received his BSc degree in automatic control from Wuhan University of Technology,China, in 2001, and the PhD degree in control theory and control engineering from Huazhong University of Science and Technology, China, in 2007. In 2011, he was a Research Fellow with the University of Hong Kong, Hong Kong, for three months, and also a Research Fellow with the City University of Hong Kong, Hong Kong, in 2012, for six months. Currently, he is a Professor with the School of Information Science and Engineering, East China University of Science and Technology, Shanghai,China. He is an associate editor for IEEE Transactions on Neural Networks and Learning Systems, International Journal of Robotics and Automation and IEEE Open Journal of Circuits and Systems. His research interests include networked control systems, multi-agent systems and robotics.

Xisheng Zhan

Xisheng Zhan is Professor at the College of Mechatronics and Control Engineering, Hubei Normal University. He received the BS and MS degrees in Control Theory and Control Engineering from the Liaoning Shihua University, Fushun, Chinain 2003 and in 2006 respectively, He received his PhD degree in Control Theory and Applications from the Department of Control Science and Engineering, Huazhong University of Science and Technology,Wuhan, China, in 2012. His research interests include networked control systems, robust control and iterative learning control.

Sha Fan

Sha Fan received the BS degree in process equipment and control engineering and MS in chemical process machinery from Kunming University of Science and Technology, Yunnan, China, in 2013 and 2016, respectively. She is currently pursuing the PhD degree in control Science and engineering with East China University of Science and Technology, Shanghai, China. Her current research interests include networked multi-sensor fusion estimation,complex networks.

Kaibo Shi

Kaibo Shi received PhD degree in School of Automation Engineering at the University of Electronic Science and Technology of China. He is a professor of School of Information Sciences and Engineering,Chengdu University. From Sep 2014 to Sep 2015, he was a visiting scholar at the Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada. He was Research Assistant with the Department of Computer and Information Science,Faculty of Science and Technology, University of Macau, Taipa, from May 2016 to Jun 2016 and Jan 2017 to Oct 2017. He was also a Visiting Scholar with the Department of Electrical Engineering, Yeungnam University,Gyeongsan, South Korea, from Dec 2019 to Jan 2020. His current research interests include stability theorem, robust control, sampled-data control systems and networked control systems.