Neurodynamic Optimization Approaches With Fixed-Time Convergence for Nash Equilibrium Seeking: Theory and Hardware Experiment

Xingxing Ju; Xinsong Yang; Chuandong Li; Gang Feng; Daniel W. C. Ho

doi:10.1109/JAS.2025.125780

IEEE/CAA Journal of Automatica Sinica

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X. Ju, X. Yang, C. Li, G. Feng, and D. Ho, “Neurodynamic optimization approaches with fixed-time convergence for Nash equilibrium seeking: Theory and hardware experiment,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 3, pp. 1–11, Mar. 2026. doi: 10.1109/JAS.2025.125780

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X. Ju, X. Yang, C. Li, G. Feng, and D. Ho, “Neurodynamic optimization approaches with fixed-time convergence for Nash equilibrium seeking: Theory and hardware experiment,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 3, pp. 1–11, Mar. 2026. doi: 10.1109/JAS.2025.125780

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Neurodynamic Optimization Approaches With Fixed-Time Convergence for Nash Equilibrium Seeking: Theory and Hardware Experiment

doi: 10.1109/JAS.2025.125780

Funds: This work was supported in part by the National Natural Science Foundation of China (62403336, 62373262, 62373310), the Research Grants Council of Hong Kong (CityU-11208223, CityU-11213023, CityU-11205724), the China Postdoctoral Science Foundation (2023M742457), the Postdoctoral Fellowship Program (Grade B) of China Postdoctoral Science Foundation (GZB20230467), and the Foundation of Key Laboratory of System Control and Information Processing of Ministry of Education of China (Scip20240107)

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Author Bio:
Xingxing Ju received the M.S. degree in operational research and control theory and the Ph.D. degree in computer science and technology from Southwest University, in 2019 and 2022, respectively. He is currently a Research Fellow with the College of Electronics and Information Engineering, Sichuan University. From October 2021 to May 2022, he was a Research Assistant with the City University of Hong Kong, China. From September 2023 to January 2024, he was a Postdoctor with the City University of Hong Kong, China. His current research interests include optimization-based control design and implementations, game theory and learning in multi-agent systems, and their applications in robotics. He was the recipient of the Outstanding Ph.D. Thesis Award of Chongqing, in 2023. He is a Member of the Youth Work Committee of the Chinese Association of Automation, and a Member of the Youth Work Committee of the Chinese Command and Control Society

Xinsong Yang received the B.S. degree in mathematics from Huaihua Normal University in 1992, and the M.S. degree in mathematics from Yunnan University in 2006. From 2006 to 2012, he was with Honghe University. From 2012 to 2020, He was a Professor with Chongqing Normal University. From 2021 to present, he is a Professor with Sichuan University. His current research interest is group intelligence and control. He is the Author or Co-Author of more than 100 papers in refereed international journals. He is the Highly Cited Researcher Award by Thomson Reuters/Clarivate Analytics from 2019 to 2024. He serves as an Associate Editor for the Neurocomputing, Neural Processing Letters, Mathematics, Frontiers in Applied Mathematics and Statistics, and Mathematical Modelling and Control. He is currently the Editor-in-Chief of the Intelligence & Control

Chuandong Li (Senior Member, IEEE) received the B.S. degree in applied mathematics from Sichuan University in 1992, and the M.S. degree in operational research and control theory and the Ph.D. degree in computer software and theory from Chongqing University, in 2001 and 2005, respectively. From 2006 to 2008, he was a Research Fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, China. He has been a Professor with the College of Electronic and Information Engineering, Southwest University, since 2012. His current research interests include computational intelligence, neural networks, memristive systems, chaos control and synchronization, and impulsive dynamical systems. He has published over 200 journal papers

Gang Feng (Fellow, IEEE) received the Ph.D. degree in electrical engineering from the Universityof Melbourne, Australia, in 1992. He has been with City University of Hong Kong, China since 2000 after serving as Lecturer/Senior Lecturer at the School of Electrical Engineering, University of New South Wales, Australia, from 1992 to 1999. He is now Chair Professor of mechatronic engineering with the Department of Biomedical Engineering, City University of Hong Kong, China. His current research interests include multi-agent systems and control, intelligent systems and control, and networked systems and control. Prof. Feng has been awarded an Alexander von Humboldt Fellowship, the IEEE Transactions on Fuzzy Systems Outstanding Paper Award, Changjiang Chair Professorship from Education Ministry of China, and CityU Outstanding Research Award. He is listed as a SCI highly cited researcher by Clarivate Analytics. He is an Associate Editor of IEEE Transactions on Fuzzy Systems, Journal of Systems Science and Complexity, and Autonomous Intelligent Systems, and was an associate editor of IEEE Transactions on Automatic Control, IEEE Transactions on Systems, Man, and Cybernetics, Part C, Mechatronics, and Journal of Control Theory and Applications. He is on the Advisory Board of Unmanned Systems

Daniel W. C. Ho (Life Fellow, IEEE) received the B.S., M.S., and Ph.D. degrees in mathematics from the University of Salford, Greater Manchester, UK, in 1980, 1982, and 1986, respectively. From 1985 to 1988, he was a Research Fellow with the Industrial Control Unit, University of Strathclyde, UK. In 1989, he joined the City University of Hong Kong, China, where he is currently a Chair Professor of applied mathematics, and Associate Dean with the College of Science. His research interests include control and estimation theory, complex dynamical distributed networks, multi-agent systems, and stochastic systems. Dr. Ho has more than 300 publications in scientific journals. He was the recipient of the Chang Jiang Chair Professor Awarded by the Ministry of Education, China in 2012, and ISI Highly Cited Researchers Award in Engineering by Clarivate Analytics, from 2014 to 2024. He has been on the Editorial Board of a number of journals including IEEE Transactions on Neural Networks and Learning Systems, IET Control Theory & Applications, Journal of the Franklin Institute, Franklin Open, and Asian Journal of Control
Corresponding author: Xinsong Yang, e-mail: xinsongyang@scu.edu.cn; Chuandong Li, e-mail: cdli@swu.edu.cn
Received Date: 2025-04-28
Revised Date: 2025-06-12
Accepted Date: 2025-08-05

Available Online: 2026-03-02

Abstract

Abstract

The convergence rate is one of the key performance measures for Nash equilibrium (NE) seeking strategies. In this work, we present several novel fast decoupled/coupled time-varying neurodynamic optimization approaches with fixed-time (FT) convergence to Nash equilibrium seeking in non-cooperative games. The dynamics trajectories are demonstrated to converge to the NE solution within a fixed time from any initial states. The proposed neurodynamic networks exhibit a faster convergence rate with appropriately selected time-varying coefficients. Additionally, the upper bounds of the convergence time of the proposed NE seeking networks are smaller than those for strategies with constant coefficients. The robustness of the proposed NE seeking neurodynamic approaches under bounded perturbations is further studied. The efficacy and practicality of the proposed NE seeking approaches are validated through simulations and field-programmable gate array (FPGA) experiments on duopoly market games.
- Fixed-time (FT) convergence,
- hardware implementation,
- Nash equilibrium (NE),
- neurodynamic optimization approaches

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References

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Neurodynamic Optimization Approaches With Fixed-Time Convergence for Nash Equilibrium Seeking: Theory and Hardware Experiment

doi: 10.1109/JAS.2025.125780

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