Attack-Resilient Distributed Nash Equilibrium Seeking for Networked Games Under Unbounded FDI Attacks: Theory and Experiment

Zhi Feng; Zhexin Shi; Xiwang Dong; Guoqiang Hu; Jinhu Lv

doi:10.1109/JAS.2025.125486

IEEE/CAA Journal of Automatica Sinica

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Z. Feng, Z. Shi, X. Dong, G. Hu, and J. Lv, “Attack-resilient distributed Nash equilibrium seeking for networked games under unbounded FDI attacks: Theory and experiment,” IEEE/CAA J. Autom. Sinica, 2025. doi: 10.1109/JAS.2025.125486

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Z. Feng, Z. Shi, X. Dong, G. Hu, and J. Lv, “Attack-resilient distributed Nash equilibrium seeking for networked games under unbounded FDI attacks: Theory and experiment,” IEEE/CAA J. Autom. Sinica, 2025. doi: 10.1109/JAS.2025.125486

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Attack-Resilient Distributed Nash Equilibrium Seeking for Networked Games Under Unbounded FDI Attacks: Theory and Experiment

doi: 10.1109/JAS.2025.125486

Funds: This work was supported in part by the National Natural Science Foundation of China (62373022, U2241217, 62141604), Beijing Natural Science Foundation (4252043, JQ23019), the Aeronautical Science Fund (2023Z034051001), the Academic Excellence Foundation of BUAA for PhD Students, the Science and Technology Innovation 2030—Key Project of New Generation Artificial Intelligence (2020AAA0108200), and the National Key Research and Development Program of China (2022YFB3305600)

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Author Bio:
Zhi Feng joined the School of Automation Science and Electrical Engineering, Beihang University, in 2022, where he is currently an Associate Professor. He received the Ph.D. degree in control science and engineering from Nanyang Technological University, Singapore, in 2017 and was a Research Fellow at Nanyang Technological University, Singapore, from 2018 to 2022. His research interests include distributed control, optimization and game theory with applications to multi-robot systems systems. He was the recipient of Best Paper in Automation Award in the 14th IEEE International Conference on Information and Automation, and finalists of Best Paper in the 7th IEEE International Conference on Real-time Computing and Robotics and the 18th IEEE International Conference on Control & Automation, 2024

Zhexin Shi received the B.E. degree in guidance, navigation, and control from Beihang University, in 2021. He is currently pursuing his Ph.D degree with the School of Automation Science and Electrical Engineering, Beihang University. His research interests include cooperative control and formation tracking of multi-agent systems

Xiwang Dong (Senior Member, IEEE) received the B.E. degree in Automation from Chongqing University, in 2009, and the Ph.D. degree in control science and engineering from Tsinghua University, in 2014. From 2014 to 2015, he was a Research Fellow with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, and from 2014 to 2018, he was a Lecturer with the School of Automation Science and Electrical Engineering, Beihang University, where he is currently a Professor. His research interests include consensus control, formation tracking and containment control of multi-agent systems with applications to UAV swarm systems. He was the recipient of the National Natural Science Fund for Excellent Young Scholars in 2019 and the Wu Wenjun Artificial Intelligence Excellent Youth Award in 2018, and 2015. His four papers received the (finalist) Best Paper Award in IEEE or IFAC conferences

Guoqiang Hu (Senior Member, IEEE) joined the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, in 2011, where he is currently a Full Professor. He was an Assistant Professor with the Department of Mechanical and Nuclear Engineering at Kansas State University, USA, from 2008 to 2011. He received the Ph.D. degree in mechanical engineering from University of Florida, USA, in 2007. His research interests include distributed control, optimization, game theory, and data science, with applications to multi-robot systems and smart city systems. He was a recipient of the Best Paper in Automation Award in the 14th IEEE International Conference on Information and Automation, and a recipient of the Guan Zhao-Zhi Award in the 36th Chinese Control Conference. He serves as Associate Editor for IEEE Transactions on Control Systems Technology, IEEE Transactions on Automatic Control and Automatica

Jinhu Lv (Fellow, IEEE) received the Ph.D. degree in applied mathematics from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, in 2002. He was a Professor with RMIT University, Australia, and a Visiting Fellow with Princeton University, USA. He is currently a Full Professor at the School of Automation Science and Electrical Engineering, Beihang University. He is also a Professor with the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He is also the Chief Scientist of the National Key Research and Development Program of China and also a Leading Scientist of Innovative Research Groups of the National Natural Science Foundation of China. His current research interests include cooperation control, complex networks, multi-agent systems and big data. He was a recipient of the Prestigious Ho Leung Ho Lee Foundation Award in 2015, the State Natural Science Award thrice from the Chinese Government in 2008, 2012, and 2016, the Australian Research Council Future Fellowships Award in 2009, the National Natural Science Fund for Distinguished Young Scholars, and a Leading Scientist of the Ten Thousand Talents Program of China, and the Highly Cited Researcher Award in engineering in 2014−2019. He was the General Co-Chair of the 43rd Annual Conference of the IEEE Industrial Electronics Society in 2017. He was an Editor in various ranks for 15 SCI journals, including the Co-Editor-in-Chief of IEEE Transactions on Industrial Informatics and seven IEEE Transactions Journals
Corresponding author: Zhi Feng, e-mail: zhifeng@buaa.edu.cn
¹ The proof follows a similar process to that of Lemma 5 in [27].
Received Date: 2025-02-08
Accepted Date: 2025-04-18

Available Online: 2025-09-09

Abstract

Abstract

An attack-resilient distributed Nash equilibrium (NE) seeking problem is addressed for noncooperative games of networked systems under malicious cyber-attacks, i.e., false data injection (FDI) attacks. Different from many existing distributed NE seeking works, it is practical and challenging to get resilient adaptively distributed NE seeking under unknown and unbounded FDI attacks. An attack-resilient NE seeking algorithm that is distributed (i.e., independent of global information on the graph’s algebraic connectivity, Lipschitz and monotone constants of pseudo-gradients, or number of players), is presented by means of incorporating the consensus-based gradient play with a distributed attack identifier so as to achieve simultaneous NE seeking and attack identification asymptotically. Another key characteristic is that FDI attacks are allowed to be unknown and unbounded. By exploiting nonsmooth analysis and stability theory, the global asymptotic convergence of the developed algorithm to the NE is ensured. Moreover, we extend this design to further consider the attack-resilient NE seeking of double-integrator players. Lastly, numerical simulation and practical experiment results are presented to validate the developed algorithms’ effectiveness.
- Adaptively distributed NE seeking,
- attack-resilient mechanism,
- noncooperative game,
- unknown FDI attack

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¹ The proof follows a similar process to that of Lemma 5 in [27].

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Attack-Resilient Distributed Nash Equilibrium Seeking for Networked Games Under Unbounded FDI Attacks: Theory and Experiment

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