Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

Maojiao Ye; Danhu Li; Qing-Long Han; Lei Ding

doi:10.1109/JAS.2022.105428

Volume 10 Issue 2

Feb. 2023

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 11.8, Top 4% (SCI Q1)

CiteScore: 17.6, Top 3% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2023 > 10(2): 376-387

M. Ye, D. Li, Q.-L. Han, and L. Ding, “Distributed Nash equilibrium seeking for general networked games with bounded disturbances,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 376–387, Feb. 2023. doi: 10.1109/JAS.2022.105428

Citation:

M. Ye, D. Li, Q.-L. Han, and L. Ding, “Distributed Nash equilibrium seeking for general networked games with bounded disturbances,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 376–387, Feb. 2023. doi: 10.1109/JAS.2022.105428

Citation:

PDF( 1933 KB)

Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

doi: 10.1109/JAS.2022.105428

Maojiao Ye^1
,,
Danhu Li^1
,,
Qing-Long Han^{2
,
,},
Lei Ding^{3
,
,}

1.
School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
2.
School of Science, Computing and Engineering Technologies, Swinburne University of Technology, Melbourne, VIC 3122, Australia
3.
Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Funds: This work was supported by the National Natural Science Foundation of China (NSFC) (62222308, 62173181, 62073171, 62221004), the Natural Science Foundation of Jiangsu Province (BK20200744, BK20220139), Jiangsu Specially-Appointed Professor (RK043STP19001), 1311 Talent Plan of Nanjing University of Posts and Telecommunications, the Young Elite Scientists SponsorshipProgram by CAST (2021QNRC001), and the Fundamental Research Funds for the Central Universities (30920032203)

More Information

Author Bio:
Maojiao Ye (Member, IEEE) received the B.Eng. degree in automation from the University of Electronic Science and Technology of China, in 2012 and the Ph.D. degree from Nanyang Technological University, Singapore, in 2016. She is currently a Professor with the School of Automaton, Nanjing University of Science and Technology. Prior to her current position, she was a Research Fellow in the School of Electrical and Electronic Engineering at Nanyang Technological University from 2016 to 2017. Her research interests include game theory, distributed optimization, and their applications. She was the recipient of Guan Zhao-Zhi Award in the 36th Chinese Control Conference 2017 (first author), and the Best Paper Award in the 15th IEEE International Conference on Control and Automation 2019 (sole author). She is an Early Career Advisory Board Member of Control Engineering Practice

Danhu Li received the B.Eng. degree in electrical engineering and automation from the Institute of Disaster Prevention, in 2019. He is currently a master student in smart grid and control at Nanjing University of Science and Technology. His research interests include game theory, robust control and their applications

Qing-Long Han (Fellow, IEEE) received the B.Sc. degree in mathematics from Shandong Normal University, in 1983, and the M.Sc. and Ph.D. degrees in control engineering from East China University of Science and Technology, in 1992 and 1997, respectively. He is Pro Vice-Chancellor (Research Quality) and a Distinguished Professor at Swinburne University of Technology, Melbourne, Australia. He held various academic and management positions at Griffith University and Central Queensland University, Australia. His research interests include networked control systems, multi-agent systems, time-delay systems, smart grids, unmanned surface vehicles, and neural networks. Professor Han was the recipient of The 2021 Norbert Wiener Award (the highest award in systems science and engineering, and cybernetics), The 2021 M. A. Sargent Medal (the highest award of the Electrical College Board of Engineers Australia), The 2021 IEEE/CAA Journal of Automatica Sinica Norbert Wiener Review Award, The 2020 IEEE Systems, Man, and Cybernetics (SMC) Society Andrew P. Sage Best Transactions Paper Award, The 2020 IEEE Transactions on Industrial Informatics Outstanding Paper Award, and The 2019 IEEE SMC Society Andrew P. Sage Best Transactions Paper Award. He is a Member of the Academia Europaea (The Academy of Europe) and a Fellow of The Institution of Engineers Australia. He is a Highly Cited Researcher in both Engineering and Computer Science (Clarivate 2019–2022). He has served as an AdCom Member of IEEE Industrial Electronics Society (IES), a Member of IEEE IES Fellow Committee, and Chair of IEEE IES Technical Committee on Networked Control Systems. He is Co-Editor-in-Chief of IEEE Transactions on Industrial Informatics, Editor-in-Chief of IEEE/CAA Journal of Automatica Sinica, Co-Editor of Australian Journal of Electrical and Electronic Engineering, an Associate Editor for 12 international journals, including the IEEE Transactions on Cybernetics, IEEE Industrial Electronics Magazine, Control Engineering Practice, and Information Sciences, and a Guest Editor for 13 Special Issues

Lei Ding (Senior Member, IEEE) received the B.Eng. degree in automation, and the M.Eng. and Ph.D. degrees in control theory and control engineering from the Dalian Maritime University, in 2007, 2009, and 2014, respectively. From 2010 to 2012, he was a Visiting Ph.D. Student sponsored by China Scholarship Council at the Centre for Intelligent and Networked Systems, Central Queensland University, Australia. From 2015 to 2016, he was a Visiting Research Fellow with Western Sydney University, Australia. From 2016 to 2017, he was a Postdoctoral Associate with Wayne State University, USA. From 2017 to 2019, he worked as a Research Fellow with the Swinburne University of Technology, Australia. He is currently a Full Professor at the Nanjing University of Posts and Telecommunications. His research interests include cooperative control of networked systems and their applications to smart grids. Professor Ding was the recipient of the 2021 IEEE/CAA Journal of Automatica Sinica Norbert Wiener Review Award, the 2020 IEEE Transactions on Industrial Informatics Outstanding Paper Award, and the 2019 IEEE Systems, Man, and Cybernetics (SMC) Society Andrew P. Sage Best Transactions Paper Award (IEEE Transactions on Cybernetics). He received the 2018 IEEE Transactions on Cybernetics Outstanding Reviewer. He is an Early Career Advisory Board Member of IEEE/CAA Journal of Automatica and Sinica and Control Engineering Practice. He has served as a Guest Editor of Control Engineering Practice, IEEE Transactions on Systems, Man, and Cybernetics: Systems, and Information Sciences; the Chair of IEEE IES Technical Committee on Network-Based Control Systems and Applications; the Technical Track Co-Chair for several international conferences
Corresponding author: Qing-Long Han, e-mail: qhan@swin.edu.au; Lei Ding, e-mail: dl522@163.com
¹ For presentation simplicity, \begin{document}$ x_i $\end{document} is supposed to be one-dimensional. It is worth mentioning that the presented methods and results are directly applicable to accommodate games with multiple dimensional actions.
Received Date: 2021-11-17
Accepted Date: 2021-12-05

Available Online: 2022-01-02

Abstract

Abstract

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information. First, reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with first-order and second-order players, respectively. In the developed algorithms, the observed disturbance values are included in control signals to eliminate the influence of disturbances, based on which a gradient-like optimization method is implemented for each player. Second, a signum function based distributed algorithm is proposed to attenuate disturbances for games with second-order integrator-type players. To be more specific, a signum function is involved in the proposed seeking strategy to dominate disturbances, based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players’ objective functions. Through Lyapunov stability analysis, it is proven that the players’ actions can approach a small region around the Nash equilibrium by utilizing disturbance observer-based strategies with appropriate control gains. Moreover, exponential (asymptotic) convergence can be achieved when the signum function based control strategy (with an adaptive control gain) is employed. The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform (V-REP) and MATLAB.
- Distributed networks,
- disturbance rejection,
- Nash equilibrium,
- networked games

FullText(HTML)

¹ For presentation simplicity, $ x_i $ is supposed to be one-dimensional. It is worth mentioning that the presented methods and results are directly applicable to accommodate games with multiple dimensional actions.

References(38)

References

[1]	N. Xiao, X. Wang, L. Xie, T. Wongpiromsarn, E. Frazzoli, and D. Rus, “Road pricing design based on game theory and multi-agent consensus,” IEEE/CAA J. Autom. Sinica, vol. 1, no. 1, pp. 31–39, 2014. doi: 10.1109/JAS.2014.7004617
[2]	M. Ye and G. Hu, “Distributed Nash equilibrium seeking by a consensus based approach,” IEEE Trans. Autom. Control, vol. 62, no. 9, pp. 4811–4818, 2017. doi: 10.1109/TAC.2017.2688452
[3]	B. Gharesifard and J. Cortes, “Distributed convergence to Nash equilibria in two-network zero-sum games,” Automatica, vol. 49, no. 6, pp. 1683–1692, 2013. doi: 10.1016/j.automatica.2013.02.062
[4]	Y. Lou, Y. Hong, L. Xie, G. Shi, and K. H. Johansson, “Nash equilibrium computation in subnetwork zero-sum games with switching communications,” IEEE Trans. Autom. Control, vol. 61, no. 10, pp. 2920–2935, 2016. doi: 10.1109/TAC.2015.2504962
[5]	J. Koshal, A. Nedic, and U.V. Shanbhag, “Distributed algorithms for aggregative games on graphs,” Oper. Res., vol. 64, no. 3, pp. 680–704, 2016. doi: 10.1287/opre.2016.1501
[6]	S. Liang, P. Yi, and Y. Hong, “Distributed Nash equilibrium seeking for aggregative games with coupled constraints,” Automatica, vol. 85, no. 85, pp. 179–185, 2017.
[7]	P. Yi and L. Pavel, “Distributed generalized Nash equilibria computation of monotone games via double-layer preconditioned proximal-point algorithms,” IEEE Trans. Control Netw. Syst., vol. 6, no. 1, pp. 299–311, 2019. doi: 10.1109/TCNS.2018.2813928
[8]	B. Huang, Y. Zou, and Z. Meng, “Distributed-observer-based Nash equilibrium seeking algorithm for quadratic games with nonlinear dynamics,” IEEE Trans. Syst. Man Cybern. Syst.,Systems, vol. 51, no. 11, pp. 7260–7268, 2021. doi: 10.1109/TSMC.2020.2968127
[9]	X. Ai, “Distributed Nash equilibrium seeking for networked games of multiple high-order systems with disturbance rejection and communication delay,” Nonlinear Dynam., vol. 101, no. 2, pp. 961–976, 2020. doi: 10.1007/s11071-020-05758-5
[10]	Y. Hua, X. Dong, Q. Li, and Z. Ren, “Distributed time-varying formation robust tracking for general linear multiagent systems with parameter uncertainties and external disturbances,” IEEE Trans. Cybern., vol. 47, no. 8, pp. 1959–1969, 2017. doi: 10.1109/TCYB.2017.2701889
[11]	Y. Chen, R. Yu, Y, Zhang, and C. Liu, “Circular formation flight control for unmanned aerial vehicles with directed network and external disturbance,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 505–516, 2020. doi: 10.1109/JAS.2019.1911669
[12]	Q. Wang and C. Sun, “Distributed asymptotic consensus in directed networks of nonaffine systems with nonvanishing disturbance,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1133–1140, 2021. doi: 10.1109/JAS.2021.1004021
[13]	G. Lin, H. Li, H. Ma, D. Yao, and R. Lu, “Human-in-the-loop consensus control for nonlinear multi-agent systems with actuator faults,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 111–122, 2022. doi: 10.1109/JAS.2020.1003596
[14]	W. Chen, J. Yang, L. Guo, and S. Li, “Disturbance-observer-based control and related methods–An overview,” IEEE Trans. Ind. Electronics, vol. 63, no. 2, pp. 1083–1095, 2016. doi: 10.1109/TIE.2015.2478397
[15]	J. Huang, S. Ri, L. Liu, Y. Yang, J. Kim, and G. Pak, “Nonlinear disturbance observer-based dynamic surface control of mobile wheeled inverted pendulum,” IEEE Trans. Control Syst. Technol., vol. 23, no. 6, pp. 2400–2407, 2015. doi: 10.1109/TCST.2015.2404897
[16]	J. Yang, S. Li, and L. Guo, “Nonlinear-disturbance-observer-based robust flight control for airbreathing hypersonic vehicles,” IEEE Trans. Aerosp. Electron. Syst., vol. 49, no. 2, pp. 1263–1275, 2013. doi: 10.1109/TAES.2013.6494412
[17]	W. Chen, “Nonlinear disturbance observer-enhanced dynamic inversion control of missiles,” J. Guid. Control Dynam., vol. 26, no. 1, pp. 161–166, 2003. doi: 10.2514/2.5027
[18]	A. Mohammadi, M. Tavakoli, H. Marquez, and F. Hashemzadeh, “Nonlinear disturbance observer design for robotic manipulators,” Control Eng. Pract., vol. 21, no. 3, pp. 253–267, 2013. doi: 10.1016/j.conengprac.2012.10.008
[19]	S. Mohammed, W. Huo, J. Huang, H. Rifai, and Y. Amirat, “Nonlinear disturbance observer based sliding mode control of a human-driven knee joint orthosis,” Robot. Auton. Syst., vol. 75, pp. 41–49, 2015.
[20]	M. Colantonio, A. Desages, J. Romagnoli, and A. Palazoglu, “Nonlinear control of a CSTR: Disturbance rejection using sliding mode control,” Ind. Eng. Chem. Res., vol. 34, no. 7, pp. 2383–2392, 1995. doi: 10.1021/ie00046a022
[21]	X. Zhang, L. Sun, K. Zhao, and L. Sun, “Nonlinear speed control for PMSM system using sliding-mode control and disturbance compensation techniques,” IEEE Trans. Power Electron., vol. 28, no. 3, pp. 1358–1365, 2013. doi: 10.1109/TPEL.2012.2206610
[22]	L. Besnard, Y. Shtessel, and B. Landrum, “Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer,” J. Franklin Inst., vol. 349, no. 2, pp. 658–684, 2012. doi: 10.1016/j.jfranklin.2011.06.031
[23]	X. Zhang and X Liu, “Further results on consensus of second-order multi-agent systems with exogenous disturbance,” IEEE Trans. Circuits Syst., vol. 60, no. 12, pp. 3215–3226, 2013. doi: 10.1109/TCSI.2013.2265978
[24]	W. Wang, H. Liang, Y. Pan, and T. Li, “Prescribed performance adaptive fuzzy containment control for nonlinear multiagent systems using disturbance observer,” IEEE Trans. Cybern., vol. 50, no. 9, pp. 3879–3891, 2020. doi: 10.1109/TCYB.2020.2969499
[25]	J. Zhang, M. Lyu, T. Shen, L. Liu, and Y. Bo, “Sliding mode control for a class of nonlinear multi-agent system with time delay and uncertainties,” IEEE Trans. Ind. Electron., vol. 65, no. 1, pp. 865–875, 2018. doi: 10.1109/TIE.2017.2701777
[26]	Z. Zhang, S. Chen, and Y. Zheng, “Fully distributed scaled consensus tracking of high-order multi-agent systems with time delays and disturbances,” IEEE Trans. IInd. Informat., vol. 18, no. 1, pp. 305–314, 2022. doi: 10.1109/TII.2021.3069207
[27]	H. Liang, X. Guo, Y. Pan, and T. Huang, “Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers,” IEEE Trans. Fuzzy Syst., vol. 29, no. 6, pp. 1601–1614, 2021. doi: 10.1109/TFUZZ.2020.2982618
[28]	H. Liang, G. Liu, H. Zhang, and T. Huang, “Neural-network-based event-triggered adaptive control of nonaffine nonlinear multiagent systems with dynamic uncertainties,” IEEE Trans. Neural Netw. Learn. Syst., vol. 32, no. 5, pp. 2239–2250, 2021. doi: 10.1109/TNNLS.2020.3003950
[29]	M. Ye, “Distributed robust seeking of Nash equilibrium for networked games: An extended-state observer based approach,” IEEE Trans. Cybern., vol. 52, no. 3, pp. 1527–1538, 2022. doi: 10.1109/TCYB.2020.2989755
[30]	X. Wang, X. Sun, A. R. Teel, and K. Liu, “Distributed robust Nash equilibrium seeking for aggregative games under persistent attacks: A hybrid systems approach,” Automatica, vol. 122, p. 109255, 2020. doi: 10.1016/j.automatica.2020.109255
[31]	Y. Zhang, S. Liang, X. Wang, and H. Ji, “Distributed Nash equilibrium seeking for aggregative games with nonlinear dynamics under external disturbances,” IEEE Trans. Cybern., vol. 50, no. 12, pp. 4876–4885, 2020. doi: 10.1109/TCYB.2019.2929394
[32]	A. Romano and L. Pavel, “Dynamic NE seeking for multi-integrator networked agents with disturbance rejection,” IEEE Trans. Control. Netw. Syst., vol. 7, no. 1, pp. 129–139, 2020. doi: 10.1109/TCNS.2019.2920590
[33]	F. L. Lewis, H. Zhang, K. Hengster-Movric, and A. Das, Cooperative Control of Multi-Agent Systems: Optimal and Adaptive Design Approaches, London, UK: Springer-Verlag, 2014.
[34]	J. Cortes, “Discontinuous dynamical systems,” IEEE Control Syst. Mag., vol. 28, no. 3, pp. 36–73, 2008. doi: 10.1109/MCS.2008.919306
[35]	L. Ding, Q.-L. Han, and X.-M. Zhang, “Distributed secondary control for active power sharing and frequency regulation in islanded microgrids using an event-triggered communication mechanism,” IEEE Trans. Ind. Informat., vol. 15, no. 7, pp. 3910–3922, 2019. doi: 10.1109/TII.2018.2884494
[36]	L. Ding, Q.-L. Han, L. Wang, and E. Sindi, “Distributed cooperative optimal control of DC microgrids with communication delays,” IEEE Trans. Ind. Informat., vol. 14, no. 9, pp. 3924–3935, 2018. doi: 10.1109/TII.2018.2799239
[37]	X.-M. Zhang, Q.-L. Han, X. Ge, D. Ding, L. Ding, D. Yue, and C. Peng, “Networked control systems: A survey of trends and techniques,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 1–17, 2020. doi: 10.1109/JAS.2019.1911861
[38]	H. Khailil, Nonlinear Systems, Upper Saddle River, USA: Prentice Hall, 2002.

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(12)

Get Citation

PDF

XML

Article Metrics

Article views (833) PDF downloads(118)

Highlights

A reduced-order disturbance observer-based approach to anti-disturbance distributed Nash equilibrium seeking for games is proposed
A signum function based distributed algorithm is proposed to attenuate disturbances for games with second-order integrator-type players
Theoretic analysis is conducted to ensure the convergence of the proposed methods

Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

doi: 10.1109/JAS.2022.105428

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Highlights

Export File

Citation

Format

Content