A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Advanced Search
Volume 10 Issue 4
Apr.  2023

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77， TOP 5
Turn off MathJax
Article Contents
Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2023  >  10(4): 931-944
Y. Xu, Y. Yuan, Z. Wang, and X. L. Li, “Noncooperative model predictive game with Markov jump graph,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 4, pp. 931–944, Apr. 2023. doi: 10.1109/JAS.2023.123129
Citation: Y. Xu, Y. Yuan, Z. Wang, and X. L. Li, “Noncooperative model predictive game with Markov jump graph,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 4, pp. 931–944, Apr. 2023. doi: 10.1109/JAS.2023.123129
shu

Noncooperative Model Predictive Game With Markov Jump Graph

doi: 10.1109/JAS.2023.123129
  • 1.

    School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China

  • 2.

    School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, and also with the School of Cybersecurity, Northwestern Polytechnical University, Xi’an 710072, China

  • 3.

    School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, and also with the Key Laboratory of Intelligent Interaction and Applications, Northwestern Polytechnical University, Ministry of Industry and Information Technology, Xi’an 710072, China

Funds:  This work was supported by the National Natural Science Foundation of China (62122063, 62073268, U22B2036, 11931015), the Young Star of Science and Technology in Shaanxi Province (2020KJXX-078), the National Science Fund for Distinguished Young Scholars (62025602), and the XPLORER PRIZE
More Information
    Abstract
  • In this paper, the distributed stochastic model predictive control (MPC) is proposed for the noncooperative game problem of the discrete-time multi-player systems (MPSs) with the undirected Markov jump graph. To reflect the reality, the state and input constraints have been considered along with the external disturbances. An iterative algorithm is designed such that model predictive noncooperative game could converge to the so-called ε-Nash equilibrium in a distributed manner. Sufficient conditions are established to guarantee the convergence of the proposed algorithm. In addition, a set of easy-to-check conditions are provided to ensure the mean-square uniform bounded stability of the underlying MPSs. Finally, a numerical example on a group of spacecrafts is studied to verify the effectiveness of the proposed method.

     

    • FullText(HTML)
  • loading
    • References(51)
  • [1]
    J. B. Cruz, M. A. Simaan, A. Gacic, H. H. Jiang, B. Letelliier, M. Li, and Y. Liu, “Game-theoretic modeling and control of a military air operation,” IEEE Trans. Aerosp. Electron. Syst., vol. 37, no. 4, pp. 1393–1405, Oct. 2001. doi: 10.1109/7.976974
    [2]
    K. Virtanen, J. Karelahti, and T. Raivio, “Modeling air combat by a moving horizon influence diagram game,” J. Guid.,Control,Dyn., vol. 29, no. 5, pp. 1080–1091, Sept.–Oct. 2006. doi: 10.2514/1.17168
    [3]
    Y. Z. Li, L. Shi, P. Cheng, J. M. Chen, and D. E. Quevedo, “Jamming attacks on remote state estimation in cyber-physical systems: A game-theoretic approach,” IEEE Trans. Autom. Control, vol. 60, no. 10, pp. 2831–2836, Oct. 2015. doi: 10.1109/TAC.2015.2461851
    [4]
    S. Grammatico, F. Parise, M. Colombino, and J. Lygeros, “Decentralized convergence to Nash equilibria in constrained deterministic mean field control,” IEEE Trans. Autom. Control, vol. 61, no. 11, pp. 3315–3329, Nov. 2016. doi: 10.1109/TAC.2015.2513368
    [5]
    H. G. Su, H. G. Zhang, H. Jiang, and Y. L. Wen, “Decentralized event-triggered adaptive control of discrete-time nonzero-sum games over wireless sensor-actuator networks with input constraints,” IEEE Trans. Neural Networks Learn. Syst., vol. 31, no. 10, pp. 4254–4266, Oct. 2020. doi: 10.1109/TNNLS.2019.2953613
    [6]
    F. X. Zhang, M. C. Zhou, L. Qi, Y. Y. Du, and H. C. Sun, “A game theoretic approach for distributed and coordinated channel access control in cooperative vehicle safety systems,” IEEE Trans. Intell. Transp. Syst., vol. 21, no. 6, pp. 2297–2309, Jun. 2020. doi: 10.1109/TITS.2019.2916214
    [7]
    X. L. Li, M. Jusup, Z. Wang, H. J. Li, L. Shi, B. Podobnik, H. E. Stanley, S. Havlin, and S. Boccaletti, “Punishment diminishes the benefits of network reciprocity in social dilemma experiments,” Proc. Natl. Acad. Sci. USA, vol. 115, no. 1, pp. 30–35, Jan. 2018. doi: 10.1073/pnas.1707505115
    [8]
    A. Nedic and A. Ozdaglar, “Distributed subgradient methods for multi-agent optimization,” IEEE Trans. Autom. Control, vol. 54, no. 1, pp. 48–61, Jan. 2009. doi: 10.1109/TAC.2008.2009515
    [9]
    B. S. Chen, W. Y. Chen, C. T. Yang, and Z. G. Yan, “Noncooperative game strategy in cyber-financial systems with Wiener and Poisson random fluctuations: LMIs-constrained MOEA approach,” IEEE Trans. Cybern., vol. 48, no. 12, pp. 3323–3336, Dec. 2018. doi: 10.1109/TCYB.2018.2869018
    [10]
    M. J. Ye, D. H. 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
    [11]
    D. Paccagnan, B. Gentile, F. Parise, M. Kamgarpour, and J. Lygeros, “Nash and Wardrop equilibria in aggregative games with coupling constraints,” IEEE Trans. Autom. Control, vol. 64, no. 4, pp. 1373–1388, Apr. 2019. doi: 10.1109/TAC.2018.2849946
    [12]
    F. Parise, B. Gentile, and J. Lygeros, “A distributed algorithm for almost-Nash equilibria of average aggregative games with coupling constraints,” IEEE Trans. Control Network Syst., vol. 7, no. 2, pp. 770–782, Jun. 2020. doi: 10.1109/TCNS.2019.2944300
    [13]
    C. De Persis and S. Grammatico, “Continuous-time integral dynamics for a class of aggregative games with coupling constraints,” IEEE Trans. Autom. Control, vol. 65, no. 5, pp. 2171–2176, May 2020. doi: 10.1109/TAC.2019.2939639
    [14]
    R. Singh and A. W. Matyszkiel, “Discontinuous Nash equilibria in a two-stage linear-quadratic dynamic game with linear constraints,” IEEE Trans. Autom. Control, vol. 64, no. 7, pp. 3074–3079, Jul. 2019. doi: 10.1109/TAC.2018.2882160
    [15]
    S. Y. Li, Y. Zhang, and Q. M. Zhu, “Nash-optimization enhanced distributed model predictive control applied to the shell benchmark problem,” Inf. Sci., vol. 170, no. 2–4, pp. 329–349, Feb. 2005. doi: 10.1016/j.ins.2004.03.008
    [16]
    L. Giovanini, “Game approach to distributed model predictive control,” IET Control Theory Appl., vol. 5, no. 15, pp. 1729–1739, Oct. 2011. doi: 10.1049/iet-cta.2010.0634
    [17]
    S. Sedaghati, F. Abdollahi, and K. Khorasani, “Model predictive and non-cooperative dynamic game fault recovery control strategies for a network of unmanned underwater vehicles,” Int. J. Control, vol. 92, no. 3, pp. 489–517, Mar. 2019. doi: 10.1080/00207179.2017.1360517
    [18]
    Z. H. Pan, Z. Q. Sun, H. B. Deng, and D. F. Li, “A multilayer graph for multiagent formation and trajectory tracking control based on MPC algorithm,” IEEE Trans. Cybern., vol. 52, no. 12, pp. 13586–13597, Dec. 2022.
    [19]
    Z. Q. Sun, C. Li, J. H. Zhang, and Y. Q. Xia, “Dynamic event-triggered MPC with shrinking prediction horizon and without terminal constraint,” IEEE Trans. Cybern., vol. 52, no. 11, pp. 12140–12149, Nov. 2022.
    [20]
    Y. Song, Z. D. Wang, S. Liu, and G. L. Wei, “N-Step MPC for systems with persistent bounded disturbances under SCP,” IEEE Trans. Syst.,Man,Cybern.: Syst., vol. 50, no. 11, pp. 4762–4772, Nov. 2020. doi: 10.1109/TSMC.2018.2862406
    [21]
    Y. Song, H. F. Lou, and S. Liu, “Distributed model predictive control with actuator saturation for Markovian jump linear system,” IEEE/CAA J. Autom. Sinica, vol. 2, no. 4, pp. 374–381, Oct. 2015. doi: 10.1109/JAS.2015.7296532
    [22]
    L. T. Xie, L. Xie, H. Y. Su, and J. D. Wang, “Polyhedral feasible set computation of MPC-based optimal control problems,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 765–770, Jul. 2018. doi: 10.1109/JAS.2018.7511126
    [23]
    T. Wang, X. Q. Xu, and X. M. Tang, “Scalable clock synchronization analysis: A symmetric noncooperative output feedback tubes-MPC approach,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1604–1626, Nov. 2020. doi: 10.1109/JAS.2020.1003363
    [24]
    G. M. Wang, Q. S. Jia, J. F. Qiao, J. Bi, and M. C. Zhou, “Deep learning-based model predictive control for continuous stirred-tank reactor system,” IEEE Trans. Neural Networks Learn. Syst., vol. 32, no. 8, pp. 3643–3652, Aug. 2021. doi: 10.1109/TNNLS.2020.3015869
    [25]
    X. X. Mi and S. Y. Li, “Event-triggered MPC design for distributed systems with network communications,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 240–250, Jan. 2018. doi: 10.1109/JAS.2016.7510154
    [26]
    F. Salehisadaghiani and L. Pave, “Distributed Nash equilibrium seeking: A gossip-based algorithm,” Automatica, vol. 72, pp. 209–216, Oct. 2016. doi: 10.1016/j.automatica.2016.06.004
    [27]
    S. L. Hu, D. Yue, X. P. Xie, and Z. P. Du, “Event-triggered H∞ stabilization for networked stochastic systems with multiplicative noise and network-induced delays,” Inf. Sci., vol. 299, pp. 178–197, Apr. 2015. doi: 10.1016/j.ins.2014.11.048
    [28]
    K. Liu, E. Fridman, K. H. Johansson, and Y. Q. Xia, “Quantized control under Round-Robin communication protocol,” IEEE Trans. Ind. Electron., vol. 63, no. 7, pp. 4461–4471, Jul. 2016. doi: 10.1109/TIE.2016.2539259
    [29]
    C. Y. Jung, H. Y. Hwang, D. K. Sung, and G. U. Hwang, “Enhanced Markov chain model and throughput analysis of the slotted CSMA/CA for IEEE 802.15.4 under unsaturated traffic conditions,” IEEE Trans. Veh. Technol., vol. 58, no. 1, pp. 473–478, Jan. 2009. doi: 10.1109/TVT.2008.923669
    [30]
    L. W. Xu, X. J. Jin, Y. Wang, Y. Liu, W. C. Zhuang, and G. D. Yin, “Stochastic stable control of vehicular platoon time-delay system subject to random switching topologies and disturbances,” IEEE Trans. Veh. Technol., vol. 71, no. 6, pp. 5755–5769, Jun. 2022. doi: 10.1109/TVT.2022.3153562
    [31]
    H. Zhao, X. W. Dai, Q. Zhang, and J. L. Ding, “Robust event-triggered model predictive control for multiple high-speed trains with switching topologies,” IEEE Trans. Veh. Technol., vol. 69, no. 5, pp. 4700–4710, May 2020. doi: 10.1109/TVT.2020.2974979
    [32]
    S. X. Wen and G. Guo, “Sampled-data control for connected vehicles with Markovian switching topologies and communication delay,” IEEE Trans. Intell. Transp. Syst., vol. 21, no. 7, pp. 2930–2942, Jul. 2020. doi: 10.1109/TITS.2019.2921781
    [33]
    M. Li, Y. Chen, and C. C. Lim, “Stability analysis of complex network control system with dynamical topology and delays,” IEEE Trans. Syst.,Man,Cybern.: Syst., vol. 51, no. 11, pp. 7228–7237, Nov. 2021. doi: 10.1109/TSMC.2020.2967102
    [34]
    K. Y. You, Z. K. Li, and L. H. Xie, “Consensus condition for linear multi-agent systems over randomly switching topologies,” Automatica, vol. 49, no. 10, pp. 3125–3132, Oct. 2013. doi: 10.1016/j.automatica.2013.07.024
    [35]
    K. Li and X. W. Mu, “Containment control of stochastic multiagent systems with semi-Markovian switching topologies,” Int. J. Robust Nonlinear Control, vol. 29, no. 14, pp. 4943–4955, Sept. 2019. doi: 10.1002/rnc.4661
    [36]
    J. Zhou, T. T. Cai, W. N. Zhou, and D. B. Tong, “Master-slave synchronization for coupled neural networks with Markovian switching topologies and stochastic perturbation,” Int. J. Robust Nonlinear Control, vol. 28, no. 6, pp. 2249–2263, Apr. 2018. doi: 10.1002/rnc.4013
    [37]
    M. L. Li and F. Q. Deng, “Necessary and sufficient conditions for consensus of continuous-time multiagent systems with Markovian switching topologies and communication noises,” IEEE Trans. Cybern., vol. 50, no. 7, pp. 3264–3270, Jul. 2020. doi: 10.1109/TCYB.2019.2919740
    [38]
    J. Huang, Z. Z. Han, X. S. Cai, and L. P. Liu, “Uniformly ultimately bounded tracking control of linear differential inclusions with stochastic disturbance,” Math. Comput. Simul., vol. 81, no. 12, pp. 2662–2672, Aug. 2011. doi: 10.1016/j.matcom.2011.05.008
    [39]
    T. Mylvaganam, M. Sassano, and A. Astolfi, “Constructive ε-Nash equilibria for nonzero-sum differential games,” IEEE Trans. Autom. Control, vol. 60, no. 4, pp. 950–965, Apr. 2015. doi: 10.1109/TAC.2014.2362334
    [40]
    Y. Yuan, P. Zhang, Z. D. Wang, and L. Guo, “On resilient strategy design of multi-tasking optimal control for state-saturated systems with nonlinear disturbances: The time-varying case,” Automatica, vol. 107, pp. 138–145, Sept. 2019. doi: 10.1016/j.automatica.2019.05.041
    [41]
    S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, UK: Cambridge University Press, 2004.
    [42]
    W. B. Dunbar and R. M. Murray, “Distributed receding horizon control for multi-vehicle formation stabilization,” Automatica, vol. 42, no. 4, pp. 549–558, Apr. 2006. doi: 10.1016/j.automatica.2005.12.008
    [43]
    A. N. Venkat, I. A. Hiskens, J. B. Rawlings, and S. J. Wright, “Distributed MPC strategies with application to power system automatic generation control,” IEEE Trans. Control Syst. Technol., vol. 16, no. 6, pp. 1192–1206, Nov. 2008. doi: 10.1109/TCST.2008.919414
    [44]
    J. R. Correa, A. S. Schulz, and N. E. Stier-Moses, “Selfish routing in capacitated networks,” Math. Oper. Res., vol. 29, no. 4, pp. 961–976, Nov. 2004. doi: 10.1287/moor.1040.0098
    [45]
    T. Alpcan, T. Baçar, R. Srikant, and E. Altman, “CDMA uplink power control as a noncooperative game,” Wireless Networks, vol. 8, no. 6, pp. 659–670, Nov. 2002. doi: 10.1023/A:1020375225649
    [46]
    Z. J. Ma, D. S. Callaway, and I. A. Hiskens, “Decentralized charging control of large populations of plug-in electric vehicles,” IEEE Trans. Control Syst. Technol., vol. 21, no. 1, pp. 67–78, Jan. 2013. doi: 10.1109/TCST.2011.2174059
    [47]
    R. Johari and J. N. Tsitsiklis, “Efficiency loss in a network resource allocation game,” Math. Oper. Res., vol. 29, no. 3, pp. 407–435, Aug. 2004. doi: 10.1287/moor.1040.0091
    [48]
    B. Kouvaritakis and M. Cannon, Model Predictive Control: Classical, Robust and Stochastic. Cham, Switzerland: Springer, 2016.
    [49]
    J. D. Luis-Delgado, B. M. Al-Hadithi, and A. Jiménez, “Design of switching hyperplanes for multi-inputs multi-outputs discrete-time linear systems,” IET Control Theory Appl., vol. 10, no. 2, pp. 126–135, Jan. 2016. doi: 10.1049/iet-cta.2015.0684
    [50]
    E. A. Hogan and H. Schaub, “Relative motion control for two-spacecraft electrostatic orbit corrections,” J. Guid.,Control,Dyn., vol. 36, no. 1, pp. 240–249, Jan. 2013. doi: 10.2514/1.56118
    [51]
    Y. Yuan, P. Zhang, Z. D. Wang, and Y. Chen, “Noncooperative event-triggered control strategy design with round-robin protocol: Applications to load frequency control of circuit systems,” IEEE Trans. Ind. Electron., vol. 67, no. 3, pp. 2155–2166, Mar. 2020. doi: 10.1109/TIE.2019.2903772
    • Related Articles
    • Supplements(0)

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(9)  / Tables(1)

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (488) PDF downloads(88) Cited by()

    Highlights

    • The noncooperative game is reformulated in the framework of MPC under state/input constraints
    • An iterative algorithm is proposed for the game such that the ε-NE can be attained distributedly
    • Sufficient conditions are given to ensure the convergence of the iterative algorithm
    • Sufficient conditions are given to ensure the mean-square uniform bounded stability of the system

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return