IEEE/CAA Journal of Automatica Sinica
Citation: | M. Ye, Q.-L. Han, L. Ding, and S. Xu, “Fully distributed Nash equilibrium seeking for high-order players with actuator limitations,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 6, pp. 1434–1444, Jun. 2023. doi: 10.1109/JAS.2022.105983 |
This paper explores the problem of distributed Nash equilibrium seeking in games, where players have limited knowledge on other players’ actions. In particular, the involved players are considered to be high-order integrators with their control inputs constrained within a pre-specified region. A linear transformation for players’ dynamics is firstly utilized to facilitate the design of bounded control inputs incorporating multiple saturation functions. By introducing consensus protocols with adaptive and time-varying gains, the unknown actions for players are distributively estimated. Then, a fully distributed Nash equilibrium seeking strategy is exploited, showcasing its remarkable properties: 1) ensuring the boundedness of control inputs; 2) avoiding any global information/parameters; and 3) allowing the graph to be directed. Based on Lyapunov stability analysis, it is theoretically proved that the proposed distributed control strategy can lead all the players’ actions to the Nash equilibrium. Finally, an illustrative example is given to validate effectiveness of the proposed method.
[1] |
Y. Wan, J. Qin, F. Li, X. Yu, and Y. Kang, “Game theoretic-based distributed charging strategy for PEVs in a smart charging station,” IEEE Trans. Smart Grid, vol. 12, no. 1, pp. 538–547, 2021. doi: 10.1109/TSG.2020.3020466
|
[2] |
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
|
[3] |
J. Koshal, A. Nedic, and U. Shanbhag, “Distributed algorithms for aggregative games on graphs,” Operations Research, vol. 64, pp. 680–704, 2016. doi: 10.1287/opre.2016.1501
|
[4] |
A. R. Romano and L. Pavel, “Dynamic NE seeking for multi-integrator networked agents with disturbance rejection,” IEEE Trans. Control Network Systems, vol. 7, no. 1, pp. 129–139, 2020. doi: 10.1109/TCNS.2019.2920590
|
[5] |
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, 2023.
|
[6] |
C. Peng, J. Wu, and E. Tian, “Stochastic event-triggered H∞ control for networked systems under denial of service attacks,” IEEE Trans. Systems, Man, and Cybernetics: Systems, vol. 52, no. 7, pp. 4200–4210, 2022.
|
[7] |
X. Dong, J. Xi, G. Lu, and Y. Zhong, “Formation control for high-order linear time-invariant multiagent systems with time delays,” IEEE Trans. Control of Network Systems, vol. 1, no. 3, pp. 232–240, 2014. doi: 10.1109/TCNS.2014.2337972
|
[8] |
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
|
[9] |
M. Ye, “Distributed Nash equilibrium seeking for games in systems with bounded control inputs,” IEEE Trans. Autom. Control, vol. 66, no. 8, pp. 3833–3839, 2021. doi: 10.1109/TAC.2020.3027795
|
[10] |
X. Ai and L. Wang, “Distributed adaptive Nash equilibrium seeking and disturbance rejection for noncooperative games of high-order nonlinear systems with input saturation and input delay,” Int. J. Robust and Nonlinear Control, vol. 31, pp. 2827–2846, 2021. doi: 10.1002/rnc.5418
|
[11] |
M. Ye and G. Hu, “Adaptive approaches for fully distributed Nash equilibrium seeking in networked games,” Automatica, vol. 129, no. 3, p. 109661, 2021.
|
[12] |
C. De Persis and S. Grammatico, “Distributed averaging integral Nash equilibrium seeking on networks,” Automatica, vol. 110, p. 108548, 2019. doi: 10.1016/j.automatica.2019.108548
|
[13] |
M. Bianchi and S. Grammatico, “Continuous-time fully distributed generalized Nash equilibrium seeking for multi-integrator agents,” Automatica, vol. 129, p. 109660, 2021. doi: 10.1016/j.automatica.2021.109660
|
[14] |
F. Lewis, H. Zhang, K. Hengster-Movric, and A. Das, Cooperative Control of Multi-Agent Systems: Optimal and Adaptive Design Approaches, Springer-Verlag London, 2014.
|
[15] |
H. J. Sussmann, E. D. Sontag, and Y. Yang, “A general result on stabilization of linear systems using bounded controls,” IEEE Trans. Autom. Control, vol. 39, no. 12, pp. 2411–2425, 1994. doi: 10.1109/9.362853
|
[16] |
X. Li, Z. Sun, Y. Tang, and H. R. Karimi, “Adaptive event-triggered consensus of multi-agent systems on directed graphs,” IEEE Trans. Autom. Control, vol. 66, no. 4, pp. 1670–1685, 2021. doi: 10.1109/TAC.2020.3000819
|
[17] |
F. Salehisadaghiani and L. Pavel, “Distributed Nash equilibrium seeking in networked graphical games,” Automatica, vol. 87, pp. 17–24, 2018. doi: 10.1016/j.automatica.2017.09.016
|
[18] |
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
|
[19] |
H. K. Khalil, Nonlinear Systems, Upper Saddle River, NJ: Prentice Hall, 2002.
|