A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 11 Issue 1
Jan.  2024

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
M. Ye, Q.-L. Han, L. Ding, S. Xu, and G. Jia, “Distributed Nash equilibrium seeking strategies under quantized communication,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 1, pp. 103–112, Jan. 2024. doi: 10.1109/JAS.2022.105857
Citation: M. Ye, Q.-L. Han, L. Ding, S. Xu, and G. Jia, “Distributed Nash equilibrium seeking strategies under quantized communication,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 1, pp. 103–112, Jan. 2024. doi: 10.1109/JAS.2022.105857

Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

doi: 10.1109/JAS.2022.105857
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), the Young Elite Scientists Sponsorship Program by CAST (2021QNRC001), 1311 Talent Plan of Nanjing University of Posts and Telecommunications, and the Fundamental Research Funds for the Central Universities (30920032203)
More Information
  • This paper is concerned with distributed Nash equilibrium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization of players’ objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized information flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respectively. Through Lyapunov stability analysis, it is shown that players’ actions can be steered to a neighborhood of the Nash equilibrium with logarithmic and uniform quantizers, and the quantified convergence error depends on the parameter of the quantizer for both undirected and directed cases. A numerical example is given to verify the theoretical results.

     

  • loading
  • [1]
    L. Ding, Q.-L. Han, B. Ning, and D. Yue, “Distributed resilient finite-time secondary control for heterogeneous battery energy storage systems under denial-of-service attacks,” IEEE Trans. Industrial Informatics, vol. 16, no. 7, pp. 4909–4919, 2020. doi: 10.1109/TII.2019.2955739
    [2]
    F. L. Lewis, H. Zhang, K. Hengster-Movric, and A. Das, Cooperative Control of Multi-Agent Systems: Optimal and Adaptive Design Approaches, Springer-Verlag London, 2014.
    [3]
    C. Deng, W. Gao, and W. Che, “Distributed adaptive fault-tolerant output regulation of heterogeneous multi-agent systems with coupling uncertainties and actuator faults,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 1098–1106, 2020. doi: 10.1109/JAS.2020.1003258
    [4]
    J. Wu, Y. Zhu, Y. Zheng, and H. Wang, “Resilient bipartite consensus of second-order multi-agent systems with event-triggered communication,” IEEE Systems Journal, 2021, DOI: 10.1109/JSYST.2021.3132623.
    [5]
    X. Ge, S. Xiao, Q.-L. Han, X.-M. Zhang, and D. Ding, “Dynamic event-triggered scheduling and platooning control co-design for automated vehicles over vehicular ad-hoc networks,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 31–46, 2022. doi: 10.1109/JAS.2021.1004060
    [6]
    J. R. Wang, Y. T. Hong, J. L. Wang, J. P. Xu, Y. Tang, Q.-L. Han, and J. Kurths, “Cooperative and competitive multi-agent systems: From optimization to games,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 763–783, 2022. doi: 10.1109/JAS.2022.105506
    [7]
    X. Ge, Q.-L. Han, J. Wang, and X.-M. Zhang, “A scalable adaptive approach to multi-vehicle formation control with obstacle avoidance,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 990–1004, 2022. doi: 10.1109/JAS.2021.1004263
    [8]
    M. Ye and G. Hu, “Distributed Nash equilibrium seeking by a consensus based approach,” IEEE Trans. Automatic Control, vol. 62, no. 9, pp. 4811–4818, 2017. doi: 10.1109/TAC.2017.2688452
    [9]
    M. Ye and G. Hu, “Adaptive approaches for fully distributed Nash equilibrium seeking in networked games,” Automatica, vol. 129, p. 109661, 2021. doi: 10.1016/j.automatica.2021.109661
    [10]
    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.
    [11]
    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
    [12]
    F. Salehisadaghiani and L. Pavel, “Distributed Nash equilibrium seeking: A gossip-based algorithm,” Automatica, vol. 72, pp. 209–216, 2016. doi: 10.1016/j.automatica.2016.06.004
    [13]
    B. Gharesifard and J. Cortes, “Distributed convergence to Nash equilibria in two-network zero-sum games,” Automatica, vol. 49, pp. 1683–1692, 2013. doi: 10.1016/j.automatica.2013.02.062
    [14]
    A. R. Ibrahim and T. Hayakawa, “Nash equilibrium seeking with second-order dynamic agents,” in Proc. IEEE Conf. Decision and Control, Miami, FL, USA, 2018, pp. 2514–2518.
    [15]
    C. Shi and G. Yang, “Distributed Nash equilibrium computation in aggregative games: An event-triggered algorithm,” Information Sciences, vol. 489, pp. 289–302, 2019. doi: 10.1016/j.ins.2019.03.047
    [16]
    X.-M. Zhang, Q.-L. Han, X. Ge, D. Ding, L. Ding, Dong 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
    [17]
    A. Kashyap, T. Basar, and R. Srikant, “Quantized consensus,” Automatica, vol. 43, pp. 1192–1203, 2007. doi: 10.1016/j.automatica.2007.01.002
    [18]
    A. Nedic, A. Olshevsky, A. Ozdaglar, and J. Tsitsiklis, “On distributed averaging algorithms and quantization effects,” IEEE Trans. Automatic Control, vol. 54, no. 11, pp. 2506–2517, 2009. doi: 10.1109/TAC.2009.2031203
    [19]
    H. Liu, M. Cao, and C. De Persis, “Quantization effects on synchronized motion of teams of mobile agents with second-order dynamics,” Systems and Control Letters, vol. 61, pp. 1157–1167, 2012. doi: 10.1016/j.sysconle.2012.08.011
    [20]
    T. Li, M. Fu, L. Xie, and J. Zhang, “Distributed consensus with limited communication data rate,” IEEE Trans. Automatic Control, vol. 56, no. 2, pp. 279–292, 2011. doi: 10.1109/TAC.2010.2052384
    [21]
    T. C. Aysal, M. J. Coates, and M. G. Rabbat, “Distributed average consensus with dithered quantization,” IEEE Trans. Signal Processing, vol. 56, no. 10, pp. 4905–4918, 2008. doi: 10.1109/TSP.2008.927071
    [22]
    X. Li, M. Z. Q. Chen, and H. Su, “Quantized consensus of multi-agent networks with sampled data and Markovian interaction links,” IEEE Trans. Cybernetics, vol. 49, no. 5, pp. 1816–1825, 2019. doi: 10.1109/TCYB.2018.2814993
    [23]
    Y. Wan, J. Yan, Z. Lin, V. Sheth, and S. K. Das, “On the structural perspective of computational effectiveness for quantized consensus in layered UAV networks,” IEEE Trans. Control of Network Systems, vol. 6, no. 1, pp. 276–288, 2019. doi: 10.1109/TCNS.2018.2813926
    [24]
    Y. Zhu, S. Li, J. Ma, and Y. Zheng, “Bipartite consensus in networks of agents with antagonistic interactions and quantization,” IEEE Trans. Circuits and Systems II: Express Briefs, vol. 65, no. 12, pp. 2012–2016, 2018. doi: 10.1109/TCSII.2018.2811803
    [25]
    Q. Wang, S. Li, W. He, and W. Zhong, “Fully distributed event-triggered bipartite consensus of linear multi-agent systems with quantized communication,” IEEE Trans. Circuits and Systems II: Express Briefs, 2022, DOI: 10.1109/TCSII.2022.3154465.
    [26]
    C. Gao, Z. Wang, X. He, and H. Dong, “Fault-tolerant consensus control for multiagent systems: An encryption-decryption Scheme,” IEEE Trans. Automatic Control, vol. 67, no. 5, pp. 2560–2567, 2022. doi: 10.1109/TAC.2021.3079407
    [27]
    C. Gao, Z. Wang, X. He, and H. Dong, “Sampled-data-based fault-tolerant consensus control for multi-agent systems: A data privacy preserving scheme,” Automatica, vol. 133, p. 109847, 2021. doi: 10.1016/j.automatica.2021.109847
    [28]
    J. Liu, Z. Yu, and D. W. C. Ho, “Distributed constrained optimization with delayed subgradient information over time-varying network under adaptive quantization,” IEEE Trans. Neural Networks and Learning Systems, 2022, DOI: 10.1109/TNNLS.2022.3172450.
    [29]
    E. Nekouei, G. Nair, and T. Alpcan, “Performance analysis of gradient-based Nash seeking algorithms under quantization,” IEEE Trans. Automatic Control, vol. 61, no. 12, pp. 3771–3783, 2016. doi: 10.1109/TAC.2016.2526598
    [30]
    S. Liu, T. Li, L. Xie, M. Fu, and J. Zhang, “Continuous-time and sampled-date-based average consensus with logarithmic quantizers,” Automatica, vol. 49, pp. 3329–3336, 2013. doi: 10.1016/j.automatica.2013.07.016
    [31]
    J. Cortes, “Discontinuous dynamical systems,” IEEE Control Systems Magazine, vol. 28, no. 3, pp. 36–73, 2008. doi: 10.1109/MCS.2008.919306
    [32]
    F. Facchinei and J. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems-Volume I, Springer, New York, NY, 2003.
    [33]
    L. Liao, H. Qi, and L. Qi, “Neurodynamical optimization,” Journal of Global Optimization, vol. 28, pp. 175–195, 2004. doi: 10.1023/B:JOGO.0000015310.27011.02
    [34]
    M. S. Stankovic, K. H. Johansson, and D. M. Stipanovic, “Distributed seeking of Nash equilibria with applications to mobile sensor networks,” IEEE Trans. Automatic Control, vol. 57, no. 4, pp. 904–919, 2012. doi: 10.1109/TAC.2011.2174678
    [35]
    H. K. Khailil, Nonlinear Systems, Upper Saddle River, NJ: Prentice Hall, 2002.

Catalog

    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

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(7)

    Article Metrics

    Article views (503) PDF downloads(86) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return