Probability-guaranteed state estimation for nonlinear delayed systems under mixed attacks

Abstract

In this paper, the problem of the networked set-membership state estimation is discussed for a class of nonlinear discrete time-varying systems subject to cyber attacks and time delays. Two forms of malicious attacks (i.e. Denial-of-Service (DoS) attack and bias injection attack) are taken into account to describe the adversary's attempt to destroy/deteriorate the system performance via communication network. It is the aim of the investigated issue to propose a set-membership state estimator ensuring the required estimation performance despite the existence of both the external mixed attacks and internal time delays. By resorting to the feasibility of a series of matrix inequalities, sufficient conditions are provided for the solvability of the addressed state estimator design problem. Furthermore, an optimisation strategy is developed with the purpose of seeking the local optimal estimator parameters. At last, a numerical simulation example is presented to demonstrate the effectiveness of the proposed theoretical algorithm.

Keywords:

• Set-membership state estimation
• cyber attacks
• mixed attack strategy
• time-varying system
• time delay

Disclosure statement

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

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 62273180], and the Ministry of Industry and Information Technology [grant number JCkY2021602B035].

Notes on contributors

Xiaojian Yi

Xiaojian Yi was born in 1987. He received the B.S. degree in control technology in 2010 from the North University of China, Taiyuan, China, and the M.S. degree in 2012 and Ph.D. degree in 2016 both in reliability engineering from Beijing Institute of Technology, Beijing, China. During 2015–2016, he was a jointly trained PhD student in the University of Ottawa, Canada, to study robot reliability and maintenance. From 2016 to 2020, he was an Associate Professor with the China North Vehicle Research Institute. He is currently an Associate Professor with the Beijing Institute of Technology, Beijing, China. He is the author of two books and more than 100 articles, and is also the holder of 8 patents. His research interests include system reliability analysis, intelligent control, fault diagnosis and health management.

Huiyang Yu

Huiyang Yu received the B.S. degree in control technology from the Beijing Institute of Technology, Beijing, China, in 2021. Currently, he is working for the M.S. degree in armament science and technology from the Beijing Institute of Technology.

Ziying Fang

Ziying Fang is working for the B.S. degree in control technology from the Beijing Institute of Technology, and will work for the M.S. degree in armament science and technology from the Beijing Institute of Technology this year.

Lifeng Ma

Lifeng Ma received the B.Sc. degree in Automation from Jiangsu University, Zhenjiang, China, in 2004 and the Ph.D. degree in Control Science and Engineering from Nanjing University of Science and Technology, Nanjing, China, in 2010. From August 2008 to February 2009, he was a Visiting Ph.D. Student in the Department of Information Systems and Computing, Brunel University London, U.K. From January 2010 to April 2010 and May 2011 to September 2011, he was a Research Associate in the Department of Mechanical Engineering, the University of Hong Kong. From March 2015 to February 2017, he was a Visiting Research Fellow at the King's College London, U.K. He is currently a Professor in the School of Automation, Nanjing University of Science and Technology, Nanjing, China. His current research interests include control and signal processing, machine learning and deep learning. He has published more than 50 papers in refereed international journals.