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 9 Issue 10
Oct.  2022

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 7.847, Top 10% (SCI Q1)
    CiteScore: 13.0, Top 5% (Q1)
    Google Scholar h5-index: 64, TOP 7
Turn off MathJax
Article Contents
M. Wang, H. T. Shi, and  C. Wang,  “Distributed cooperative learning for discrete-time strict-feedback multi agent systems over directed graphs,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1831–1844, Oct. 2022. doi: 10.1109/JAS.2022.105542
Citation: M. Wang, H. T. Shi, and  C. Wang,  “Distributed cooperative learning for discrete-time strict-feedback multi agent systems over directed graphs,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1831–1844, Oct. 2022. doi: 10.1109/JAS.2022.105542

Distributed Cooperative Learning for Discrete-Time Strict-Feedback Multi Agent Systems Over Directed Graphs

doi: 10.1109/JAS.2022.105542
Funds:  This work was supported in part by the Guangdong Natural Science Foundation (2019B151502058), in part by the National Natural Science Foundation of China (61890922, 61973129), in part by the Major Key Project of PCL (PCL2021A09), and in part by the Guangdong Basic and Applied Basic Research Foundation (2021A1515012004)
More Information
  • This paper focuses on the distributed cooperative learning (DCL) problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs. Compared with the previous DCL works based on undirected graphs, two main challenges lie in that the Laplacian matrix of directed graphs is nonsymmetric, and the derived weight error systems exist n-step delays. Two novel lemmas are developed in this paper to show the exponential convergence for two kinds of linear time-varying (LTV) systems with different phenomena including the nonsymmetric Laplacian matrix and time delays. Subsequently, an adaptive neural network (NN) control scheme is proposed by establishing a directed communication graph along with n-step delays weight updating law. Then, by using two novel lemmas on the extended exponential convergence of LTV systems, estimated NN weights of all agents are verified to exponentially converge to small neighbourhoods of their common optimal values if directed communication graphs are strongly connected and balanced. The stored NN weights are reused to structure learning controllers for the improved control performance of similar control tasks by the “mod” function and proper time series. A simulation comparison is shown to demonstrate the validity of the proposed DCL method.

     

  • loading
  • [1]
    L. X. Wang and J. M. Mendel, “Generating fuzzy rules by learning from examples,” IEEE Trans. Syst.,Man,Cybern., vol. 22, no. 6, pp. 1414–1427, 1992. doi: 10.1109/21.199466
    [2]
    K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Trans. Neural Netw., vol. 1, no. 1, pp. 4–27, 1990. doi: 10.1109/72.80202
    [3]
    S. Tong and Y. Li, “Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems,” Sci. China Inf. Sci., vol. 57, no. 1, pp. 1–14, 2014.
    [4]
    T. Gao, Y.-J. Liu, L. Liu, and D. Li, “Adaptive neural network-based control for a class of nonlinear pure-feedback systems with time-varying full state constraints,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 923–933, 2018. doi: 10.1109/JAS.2018.7511195
    [5]
    X. Yang and H. He, “Adaptive critic designs for event-triggered robust control of nonlinear systems with unknown dynamics,” IEEE Trans. Cybern., vol. 49, no. 6, pp. 2255–2267, 2019. doi: 10.1109/TCYB.2018.2823199
    [6]
    B. Luo, Y. Yang, and D. Liu, “Adaptive Q-learning for data-based optimal output regulation with experience replay,” IEEE Trans. Cybern., vol. 48, no. 12, pp. 3337–3348, 2018. doi: 10.1109/TCYB.2018.2821369
    [7]
    C. Wang, D. J. Hill, S. S. Ge, and G. Chen, “An ISS-modular approach for adaptive neural control of pure-feedback systems,” Automatica, vol. 42, no. 5, pp. 723–731, 2006. doi: 10.1016/j.automatica.2006.01.004
    [8]
    X. Wang, D. Ding, H. Dong, and X.-M. Zhang, “Neural-network-based control for discrete-time nonlinear systems with input saturation under stochastic communication protocol,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 4, pp. 766–778, 2021.
    [9]
    P. C. Yeh and P. V. Kokotovic, “Adaptive control of a class of nonlinear discrete-time systems,” Int. J. Control, vol. 62, no. 2, pp. 303–324, 1995. doi: 10.1080/00207179508921545
    [10]
    A. Sahoo, H. Xu, and S. Jagannathan, “Adaptive neural network-based event-triggered control of single-input single-output nonlinear discretetime systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 1, pp. 151–164, 2016. doi: 10.1109/TNNLS.2015.2472290
    [11]
    Y.-J. Liu, S. Li, S. C. Tong, and C. L. P. Chen, “Adaptive reinforcement learning control based on neural approximation for nonlinear discretetime systems with unknown nonaffine dead-zone input,” IEEE Trans. Neural Netw. Learn. Syst., vol. 30, no. 1, pp. 295–305, 2019. doi: 10.1109/TNNLS.2018.2844165
    [12]
    S. S. Ge, G. Y. Li, and T. H. Lee, “Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems,” Automatica, vol. 39, no. 5, pp. 807–819, 2003. doi: 10.1016/S0005-1098(03)00032-3
    [13]
    S. S. Ge, C. Yang, and T. H. Lee, “Adaptive predictive control using neural network for a class of pure-feedback systems in discrete time,” IEEE Trans. Neural Netw., vol. 19, no. 9, pp. 1599–1614, 2008. doi: 10.1109/TNN.2008.2000446
    [14]
    J. Vance and S. Jagannathan, “Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form,” Automatica, vol. 44, no. 4, pp. 1020–1027, 2008. doi: 10.1016/j.automatica.2007.08.008
    [15]
    M. Wang, Z. Wang, Y. Chen, and W. Sheng, “Event-based adaptive neural tracking control for discrete-time stochastic nonlinear systems: a triggering threshold compensation strategy,” IEEE Trans. Neural Netw. Learn. Syst., vol. 31, no. 6, pp. 1968–1981, 2020. doi: 10.1109/TNNLS.2019.2927595
    [16]
    M. Wang, Z. Wang, H. Dong, and Q.-L. Han, “A novel framework for backstepping-based control of discrete-time strict-feedback nonlinear systems with multiplicative noises,” IEEE Trans. Autom. Control, vol. 66, no. 4, pp. 1484–1496, 2021. doi: 10.1109/TAC.2020.2995576
    [17]
    S.-L. Dai, S. He, M. Wang, and C. Yuan, “Adaptive neural control of underactuated surface vessels with prescribed performance guarantees,” IEEE Trans. Neural Netw. Learn. Syst., vol. 30, no. 12, pp. 3686–3698, 2019. doi: 10.1109/TNNLS.2018.2876685
    [18]
    J. Zhang, C. Sun, R. Zhang, and C. Qian, “Adaptive sliding mode control for re-entry attitude of near space hypersonic vehicle based on backstepping design,” IEEE/CAA J. Autom. Sinica, vol. 2, no. 1, pp. 94–101, 2015. doi: 10.1109/JAS.2015.7032910
    [19]
    Q. Zhou, S. Zhao, H. Li, R. Lu, and C. Wu, “Adaptive neural network tracking control for robotic manipulators with dead zone,” IEEE Trans. Neural Netw. Learn. Syst., vol. 30, no. 12, pp. 3611–3620, 2019. doi: 10.1109/TNNLS.2018.2869375
    [20]
    W. He, Z. Li, and C. L. P. Chen, “A survey of human-centered intelligent robots: issues and challenges,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 4, pp. 602–609, 2017. doi: 10.1109/JAS.2017.7510604
    [21]
    M. Wang, L. Wang, R. Huang, and C. Yang, “Event-based disturbance compensation control for discrete-time SPMSM with mismatched disturbances,” Int. Journal of Systems Science, vol. 52, no. 4, pp. 785–804, 2021. doi: 10.1080/00207721.2020.1840650
    [22]
    P. J. Antsaklis and A. Rahnama, “Control and machine intelligence for system autonomy,” J. Intell. Robot. Syst, vol. 91, no. 1, pp. 23–34, 2018. doi: 10.1007/s10846-018-0832-6
    [23]
    K. S. Fu, “Learning control systems and intelligent control systems: an intersection of artificial intelligence and automatic control,” IEEE Trans. Autom. Control, vol. 16, no. 1, pp. 70–72, 1971. doi: 10.1109/TAC.1971.1099633
    [24]
    C. Wang and D. J. Hill, “Learning from neural control,” IEEE Trans. Neural Netw., vol. 17, no. 1, pp. 130–146, 2006. doi: 10.1109/TNN.2005.860843
    [25]
    M. Wang, C. Wang, P. Shi, and X. Liu, “Dynamic learning from neural control for strict-feedback systems with guaranteed predefined performance,” IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 12, pp. 2564–2576, 2016. doi: 10.1109/TNNLS.2015.2496622
    [26]
    M. Wang, Y. Zhang, and C. Wang, “Learning from neural control for non-affine systems with full state constraints using command filtering,” Int. J. Control, vol. 93, no. 10, pp. 2392–2406, 2020. doi: 10.1080/00207179.2018.1558285
    [27]
    J. Zhang, C. Yuan, C. Wang, P. Stegagno, and W. Zeng, “Composite adaptive NN learning and control for discrete-time nonlinear uncertain systems in normal form,” Neurocomputing, vol. 390, pp. 168–184, 2020. doi: 10.1016/j.neucom.2020.01.052
    [28]
    J. Zhang, C. Yuan, P. Stegagno, H. He, and C. Wang, “Small fault detection of discrete-time nonlinear uncertain systems,” IEEE Trans. Cybern., vol. 51, no. 2, pp. 750–764, 2021. doi: 10.1109/TCYB.2019.2945629
    [29]
    S.-L. Dai, C. Wang, and M. Wang, “Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 1, pp. 111–123, 2014. doi: 10.1109/TNNLS.2013.2257843
    [30]
    C. Yang, X. Wang, L. Cheng, and H. Ma, “Neural-learning based telerobot control with guaranteed performance,” IEEE Trans. Cybern., vol. 47, no. 10, pp. 3148–3159, 2017.
    [31]
    K. You and L. Xie, “Network topology and communication data rate for consensusability of discrete-time multi-agent systems,” IEEE Trans. Autom. Control, vol. 56, no. 10, pp. 2262–2275, 2011. doi: 10.1109/TAC.2011.2164017
    [32]
    A. Amini, A. Asif, and A. Mohammadi, “Formation-containment control using dynamic event-triggering mechanism for multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 5, pp. 1235–1248, 2020.
    [33]
    B. Ning, Q.-L. Han, Z. Zuo, J. Jin, and J. Zheng, “Collective behaviors of mobile robots beyond the nearest neighbor rules with switching topology,” IEEE Trans. Cybern., vol. 48, no. 5, pp. 1577–1590, 2018. doi: 10.1109/TCYB.2017.2708321
    [34]
    S. He, M. Wang, S.-L. Dai, and F. Luo, “Leader-follower formation control of USVs with prescribed performance and collision avoidance,” IEEE Trans. Ind. Informa., vol. 15, no. 1, pp. 572–581, 2019. doi: 10.1109/TII.2018.2839739
    [35]
    R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1520–1533, 2004. doi: 10.1109/TAC.2004.834113
    [36]
    L. Liu, L. Ma, J. Zhang, and Y. Bo, “Distributed non-fragile setmembership filtering for nonlinear systems under fading channels and bias injection attacks,” Int. Journal of Systems Science, vol. 52, no. 6, pp. 1192–1205, 2021. doi: 10.1080/00207721.2021.1872118
    [37]
    W. Chen, S. Hua, and S. S. Ge, “Consensus-based distributed cooperative learning control for a group of discrete-time nonlinear multiagent systems using neural networks,” Automatica, vol. 50, no. 9, pp. 2254–2268, 2014. doi: 10.1016/j.automatica.2014.07.020
    [38]
    W. Chen, S. Hua, and H. Zhang, “Consensus-based distributed cooperative learning from closed-loop neural control systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 2, pp. 331–345, 2015. doi: 10.1109/TNNLS.2014.2315535
    [39]
    F. Gao, W. Chen, Z. Li, J. Li, and B. Xu, “Neural network-based distributed cooperative learning control for multiagent systems via eventtriggered communication,” IEEE Trans. Neural Netw. Learn. Syst., vol. 31, no. 2, pp. 407–419, 2020. doi: 10.1109/TNNLS.2019.2904253
    [40]
    S.-L. Dai, S. He, Y. Ma, J. Li, and C. Yuan, “Distributed cooperative learning control of uncertain multiagent systems with prescribed performance and preserved connectivity,” IEEE Trans. Neural Netw. Learn. Syst., vol. 32, no. 7, pp. 3217–3229, 2021. doi: 10.1109/TNNLS.2020.3010690
    [41]
    M. Abdelatti, C. Yuan, W. Zeng, and C. Wang, “Cooperative deterministic learning control for a group of homogeneous nonlinear uncertain robot manipulators”, Sci. China Inf. Sci., vol. 61, no. 11, pp. 112201, 2018.
    [42]
    C. Yuan, H. He, and C. Wang, “Cooperative deterministic learning based formation control for a group of nonlinear uncertain mechanical systems,” IEEE Trans. Ind. Informat., vol. 15, no. 1, pp. 319–333, 2019. doi: 10.1109/TII.2018.2792455
    [43]
    W. Yu, G. Chen, and M. Cao, “Consensus in directed networks of agents with nonlinear dynamics,” IEEE Trans. Autom. Control, vol. 56, no. 6, pp. 1436–1441, 2011. doi: 10.1109/TAC.2011.2112477
    [44]
    J. Ni, P. Shi, Y. Zhao, and Z. Wu, “Fixed-time output consensus tracking for high-order multi-agent systems with directed network topology and packet dropout,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 4, pp. 817–836, 2021. doi: 10.1109/JAS.2021.1003916
    [45]
    Q. Wei, X. Wang, X. Zhong, and N. Wu, “Consensus control of leaderfollowing multi-agent systems in directed topology with heterogeneous disturbances,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 423–431, 2021. doi: 10.1109/JAS.2021.1003838
    [46]
    D. Lee and M. W. Spong, “Stable flocking of multiple inertial agents on balanced graphs,” IEEE Trans. Autom. Control, vol. 52, no. 8, pp. 1469–1475, 2007. doi: 10.1109/TAC.2007.902752
    [47]
    W. Chen and W. Ren, “Event-triggered zero-gradient-sum distributed consensus optimization over directed networks,” Automatica, vol. 65, pp. 90–97, 2016. doi: 10.1016/j.automatica.2015.11.015
    [48]
    R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1987.
    [49]
    T. Zheng, C. Wang, “Relationship between persistent excitation levels and RBF network structures, with application to performance analysis of deterministic learning,” IEEE Trans. Cybern., vol. 47, no. 10, pp. 3380–3392, 2017. doi: 10.1109/TCYB.2017.2710284
    [50]
    H. K. Khalil, Nonlinear Systems. New Jersey, NJ, USA: Prentice-Hall, vol. 3, 1996.

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(10)  / Tables(1)

    Article Metrics

    Article views (755) PDF downloads(135) Cited by()

    Highlights

    • Two novel lemmas are developed in this paper to show the exponential convergence for two kinds of linear time-varying systems with different phenomena including the nonsymmetric system matrix and time delays
    • A novel distributed cooperative learning scheme is proposed for discrete-time strict-feedback multi-agent systems under strongly connected and directed balanced graphs, which breaks through the bottleneck of DCL on undirected graphs and the normal structure
    • The proposed distributed cooperative learning scheme not only ensures that the designed adaptive neural controllers can complete tracking control tasks of all the agents, but also ensures that the neural weights converge to their common ideal values. This trait reflects the learning ability of adaptive neural control from historical experiences of itself and other agents

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return