Protection-Strategy-Based Distributed State Estimation for Nonlinear Complex Networks Against Random False Data Injection Attacks

Jun Hu; Bingxin Lei; Raquel Caballero-Águila; Hongli Dong

doi:10.1109/JAS.2025.125951

Volume 13 Issue 7

Jul. 2026

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(7): 1657-1672

J. Hu, B. Lei, R. Caballero-Águila, and H. Dong, “Protection-strategy-based distributed state estimation for nonlinear complex networks against random false data injection attacks,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 7, pp. 1657–1672, Jul. 2026. doi: 10.1109/JAS.2025.125951

Citation:

J. Hu, B. Lei, R. Caballero-Águila, and H. Dong, “Protection-strategy-based distributed state estimation for nonlinear complex networks against random false data injection attacks,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 7, pp. 1657–1672, Jul. 2026. doi: 10.1109/JAS.2025.125951

Citation:

J. Hu, B. Lei, R. Caballero-Águila, and H. Dong, “Protection-strategy-based distributed state estimation for nonlinear complex networks against random false data injection attacks,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 7, pp. 1657–1672, Jul. 2026. doi: 10.1109/JAS.2025.125951

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Protection-Strategy-Based Distributed State Estimation for Nonlinear Complex Networks Against Random False Data Injection Attacks

doi: 10.1109/JAS.2025.125951

Funds: This work was supported in part by the National Natural Science Foundation of China (12171124, 12471416), the Natural Science Foundation of Heilongjiang Province of China (PL2024F015), the MCIN/AEI/10.13039/501100011033 and “ERDF a Way of Making Europe” (PID2021-124486NB-I00), and the Alexander von Humboldt Foundation of Germany

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Author Bio:
Jun Hu (Senior Member, IEEE) received the B.Sc. degree in information and computing science and M.Sc. degree in applied mathematics from Harbin University of Science and Technology in 2006 and 2009, respectively, and the Ph.D. degree in control science and engineering from Harbin Institute of Technology in 2013. From September 2010 to September 2012, he was a visiting Ph.D. student in the Department of Information Systems and Computing, Brunel University London, Uxbridge, U.K. From May 2014 to April 2016, he was an Alexander von Humboldt Research Fellow at the University of Kaiserslautern, Kaiserslautern, Germany. From January 2018 to January 2021, he was a Research Fellow at University of South Wales, Pontypridd, U.K. He is currently a Professor with the Department of Mathematics and the School of Automation, Harbin University of Science and Technology. His research interests include nonlinear control, optimized filtering and fault estimation, time-varying systems, and complex networks. He has published more than 90 papers in refereed international journals. Dr. Hu serves as a Reviewer for Mathematical Reviews, as an Editor for Neurocomputing, Systems Science & Control Engineering, and as a Guest Editor for International Journal of General Systems and Information Fusion

Bingxin Lei received the B.Sc. degree in mathematics and applied mathematics from Harbin University in 2022, and the M.Sc. degree in mathematics from Harbin University of Science and Technology in 2025. She is currently working toward the Ph.D. degree in mathematics from Harbin University of Science and Technology. Her current research interests include optimized distributed state estimation, network security, analysis and design of time-varying complex networks. She is an active Reviewer for many international journals

Raquel Caballero-Águila received the B.Sc. degree in mathematics and the Ph.D. degree in mathematical sciences, both from the University of Granada (Granada, Spain), in 1997 and 1999, respectively. In 1997, she joined the University of Jaén (Jaén, Spain), where she is currently a Professor with the Department of Statistics and Operations Research. She has authored or co-authored more than eighty papers in peer-reviewed international journals. Her research interests include time-varying stochastic systems, complex networks, filtering, prediction, and smoothing. She is a Reviewer of Mathematical Reviews and serves on the editorial boards of Systems Science and Control Engineering, and Mathematical Problems in Engineering

Hongli Dong (Senior Member, IEEE) received the Ph.D. degree in control science and engineering from Harbin Institute of Technology in 2012. From 2009 to 2010, she was a Research Assistant with the Department of Applied Mathematics, City University of Hong Kong, Hong Kong, China. From 2010 to 2011, she was a Research Assistant with the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China. From 2011 to 2012, she was a Visiting Scholar with the Department of Information Systems and Computing, Brunel University London, Uxbridge, U.K. From 2012 to 2014, she was an Alexander von Humboldt Research Fellow with the University of Duisburg-Essen, Duisburg, Germany. She is currently a Professor with the Artificial Intelligence Energy Research Institute, Northeast Petroleum University. She is also the Director of the Heilongjiang Provincial Key Laboratory of Networking and Intelligent Control. Her current research interests include robust control and networked control systems. Dr. Dong is a very active Reviewer for many international journals
Corresponding author: Jun Hu, e-mail: jhu@hrbust.edu.cn
Received Date: 2025-05-01
Revised Date: 2025-09-10
Accepted Date: 2025-10-03

Available Online: 2026-07-22

Abstract

Abstract

This paper addresses the protection-strategy-based distributed state estimation (SE) problem for time-varying nonlinear complex networks, where uncertain inner coupling and random false data injection attacks are considered. Owing to the fact that the measurement signals can be easily injected with false data by potential attackers before being transmitted to the estimator, a novel protection strategy is firstly proposed from the perspective of the defender to mitigate the effects of malicious attacks on the estimation performance. Based on the proposed protection strategy, more suspicious and unreliable measurements received are identified and discarded respectively. Accordingly, the zero-order holder strategy is employed to compensate for the discarded measurements. Subsequently, the purpose of this paper is to design a protection-strategy-based distributed SE scheme such that an optimized upper bound (UB) on the estimation error covariance (EEC) is obtained. Furthermore, a sufficient criterion is provided to guarantee the uniform boundedness of UB on the EEC. Finally, a localization problem involving multiple mobile robots is used to demonstrate the effectiveness and practicality of proposed variance-constrained optimized SE method.
- Boundedness analysis,
- protection strategy,
- random false data injection attacks,
- time-varying nonlinear complex networks,
- uncertain inner coupling (UIC)

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