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 8 Issue 2
Feb.  2021

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
Qinglai Wei, Xin Wang, Xiangnan Zhong and Naiqi Wu, "Consensus Control of Leader-Following Multi-Agent Systems in Directed Topology With Heterogeneous Disturbances," IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 423-431, Feb. 2021. doi: 10.1109/JAS.2021.1003838
Citation: Qinglai Wei, Xin Wang, Xiangnan Zhong and Naiqi Wu, "Consensus Control of Leader-Following Multi-Agent Systems in Directed Topology With Heterogeneous Disturbances," IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 423-431, Feb. 2021. doi: 10.1109/JAS.2021.1003838

Consensus Control of Leader-Following Multi-Agent Systems in Directed Topology With Heterogeneous Disturbances

doi: 10.1109/JAS.2021.1003838
Funds:  This work was supported in part by the National Natural Science Foundation of China (61722312, 61533017, 62073321) and the National Key Research and Development Program of China (2018YFB1702300)
More Information
  • This paper investigates the consensus problem for linear multi-agent systems with the heterogeneous disturbances generated by the Brown motion. Its main contribution is that a control scheme is designed to achieve the dynamic consensus for the multi-agent systems in directed topology interfered by stochastic noise. In traditional ways, the coupling weights depending on the communication structure are static. A new distributed controller is designed based on Riccati inequalities, while updating the coupling weights associated with the gain matrix by state errors between adjacent agents. By introducing time-varying coupling weights into this novel control law, the state errors between leader and followers asymptotically converge to the minimum value utilizing the local interaction. Through the Lyapunov directed method and Itô formula, the stability of the closed-loop system with the proposed control law is analyzed. Two simulation results conducted by the new and traditional schemes are presented to demonstrate the effectiveness and advantage of the developed control method.

     

  • loading
  • [1]
    A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 988–1001, Jun. 2003. doi: 10.1109/TAC.2003.812781
    [2]
    T. Wang, M. Hu, and Y. L. Zhao, “Consensus control with a constant gain for discrete-time binary-valued multi-agent systems based on a projected empirical measure method,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1052–1059, Jul. 2019. doi: 10.1109/JAS.2019.1911594
    [3]
    C. X. Shi, G. H. Yang, and X. J. Li, “Data-based fault-tolerant consensus control for uncertain multiagent systems via weighted edge dynamics,” IEEE Trans. Syst.,Man,Cybernet.:Syst., vol. 49, no. 12, pp. 2548–2558, Dec. 2019. doi: 10.1109/TSMC.2017.2743261
    [4]
    M. Yu, C. Song, F. C. Lv, K. Q. Jin, and W. Tan, “Event-triggered consensus approach for distributed battery energy storage systems,” IET Generat.,Trans. Distribut., vol. 13, no. 22, pp. 5102–5108, Nov. 2019. doi: 10.1049/iet-gtd.2018.6405
    [5]
    T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, “Novel type of phase transition in a system of self-driven particles,” Phys. Rev. Lett., vol. 75, no. 6, pp. 1226–1229, Aug. 1995. doi: 10.1103/PhysRevLett.75.1226
    [6]
    A. J. Wang, X. F. Liao, and H. B. He, “Event-triggered differentially private average consensus for multi-agent network,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 75–83, Jan. 2019. doi: 10.1109/JAS.2019.1911327
    [7]
    X. M. Li, Q. Zhou, P. S. Li, H. Y. Li, and R. Q. Lu, “Event-triggered consensus control for multi-agent systems against false data-injection attacks,” IEEE Trans. Cybernet., vol. 50, no. 5, pp. 1856–1866, May 2019.
    [8]
    Z. Wang, M. He, T. Zheng, Z. L. Fan, and G. B. Liu, “Guaranteed cost consensus for high-dimensional multi-agent systems with time-varying delays,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 181–189, Jan. 2018. doi: 10.1109/JAS.2017.7510430
    [9]
    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, Sep. 2004. doi: 10.1109/TAC.2004.834113
    [10]
    J. X. Xi, C. Wang, H. Liu, and L. Wang, “Completely distributed guaranteed-performance consensualization for high-order multiagent systems with switching topologies,” IEEE Trans. Syst.,Man,Cybernet.:Syst., vol. 49, no. 7, pp. 1338–1348, Jul. 2019. doi: 10.1109/TSMC.2018.2852277
    [11]
    W. C. Huang, Y. W. Huang, and S. B. Chen, “Robust consensus control for a class of second-order multi-agent systems with uncertain topology and disturbances,” Neurocomputing, vol. 313, pp. 426–435, Nov. 2018. doi: 10.1016/j.neucom.2018.06.013
    [12]
    Q. K. Shen, P. Shi, J. W. Zhu, and L. P. Zhang, “Adaptive consensus control of leader-following systems with transmission nonlinearities,” Int. J. Control, vol. 92, no. 2, pp. 317–328, 2019. doi: 10.1080/00207179.2017.1352104
    [13]
    K. Li, C. C. Hua, X. You, and X. P. Guan, “Output feedback-based consensus control for nonlinear time delay multiagent systems,” Automatica, vol. 111, pp. 108669, Jan. 2020. doi: 10.1016/j.automatica.2019.108669
    [14]
    H. Y. Yang, F. Y. Wang, and F. J. Han, “Containment control of fractional order multi-agent systems with time delays,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 3, pp. 727–732, May 2018. doi: 10.1109/JAS.2016.7510211
    [15]
    P. Ignaciuk and L Wieczorek, “Networked base-stock inventory control in complex distribution systems,” Mathem. Prob. Eng., vol. 2019, pp. 3754367, Nov. 2019.
    [16]
    J. Liu, Y. Yu, Q. Wang, and C. Y. Sun, “Fixed-time event-triggered consensus control for multi-agent systems with nonlinear uncertainties,” Neurocomputing, vol. 260, pp. 497–504, Oct. 2017. doi: 10.1016/j.neucom.2017.04.061
    [17]
    M. Yu, C. Yan, D. M. Xie, and G. M. Xie, “Event-triggered tracking consensus with packet losses and time-varying delays,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 2, pp. 165–173, Apr. 2016. doi: 10.1109/JAS.2016.7451104
    [18]
    Q. L. Wei, H. Y. Li, and F. -Y. Wang, “Parallel control for continuous-time linear systems: A case study,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 919–928, Jul. 2020. doi: 10.1109/JAS.2020.1003216
    [19]
    Q. L. Wei, H. Y. Li, X. Yang, and H. B. He, “Continuous-time distributed policy iteration for multicontroller nonlinear systems,” IEEE Trans. Cybernet., Apr. 2020, DOI: 10.1109/TCYB.2020.2979614.
    [20]
    Q. L. Wei, L. X. Wang, Y. Liu, and M. M. Polycarpou, “Optimal elevator group control via deep asynchronous actor-critic learning,” IEEE Trans. Neural Netw. Learn. Syst., Feb. 2020, DOI: 10.1109/TNNLS.2020.2965208.
    [21]
    Q. L. Wei, Z. H. Liao, Z. Y. Yang, B. K. Li, and D. R. Liu, “Continuous-time time-varying policy iteration, ” IEEE Trans. Cybernet., Jul. 2019, DOI: 10.1109/TCYB.2019.2926631.
    [22]
    Q. L. Wei, R. Z. Song, Z. H. Liao, B. K. Li, and F. L. Lewis, “Discrete-time impulsive adaptive dynamic programming,” IEEE Trans. Cybernet., vol. 50, no. 10, pp. 4293–4306, Oct. 2020. doi: 10.1109/TCYB.2019.2906694
    [23]
    Q. L. Wei, D. R. Liu, and F. L. Lewis, “Optimal distributed synchronization control for continuous-time heterogeneous multi-agent differential graphical games,” Inf. Sci., vol. 317, pp. 96–113, Oct. 2015. doi: 10.1016/j.ins.2015.04.044
    [24]
    H. P. Zhang, D. Yue, C. X. Dou, W. Zhao, and X. P. Xie, “Data-driven distributed optimal consensus control for unknown multiagent systems with input-delay,” IEEE Trans. Cybernet., vol. 49, no. 6, pp. 2095–2105, Jun. 2019. doi: 10.1109/TCYB.2018.2819695
    [25]
    H. G. Zhang, L. Jiang, J. H. Liu, and F. M. Qu, “Data recovery of magnetic flux leakage data gaps using multifeature conditional risk,” IEEE Trans. Autom. Sci. Eng., Jun. 2020, DOI: 10.1109/TASE.2020.2994659.
    [26]
    H. G. Zhang, Y. Liu, and Y. C. Wang, “Observer-based finite-time adaptive fuzzy control for nontriangular nonlinear systems with full-state constraints,” IEEE Trans. Cybernet., Apr. 2020, DOI: 10.1109/TCYB.2020.2984791.
    [27]
    H. G. Zhang, Y. Liu, J. Dai, and Y. C. Wang, “Command filter based adaptive fuzzy finite-time control for a class of uncertain nonlinear systems with hysteresis,” IEEE Trans. Fuzzy Syst., Jun. 2020, DOI: 10.1109/TFUZZ.2020.3003499.
    [28]
    Z. K. Li, Z. S. Duan, G. R. Chen, and L. Huang, “Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint,” IEEE Trans. Circuits Syst. I:Regular Papers, vol. 57, no. 1, pp. 213–224, Jan. 2010. doi: 10.1109/TCSI.2009.2023937
    [29]
    A. Elahi, A. Alfi, and H. Modares, “H consensus control of discretetime multi-agent systems under network imperfections and external disturbance,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 667–675, May 2019. doi: 10.1109/JAS.2019.1911474
    [30]
    X. X. Zhang and X. P. Liu, “Further results on consensus of second-order multi-agent systems with exogenous disturbance,” IEEE Trans. Circuits Syst. I:Regular Papers, vol. 60, no. 12, pp. 3215–3226, Dec. 2013. doi: 10.1109/TCSI.2013.2265978
    [31]
    H. Q. Lin, Q. L. Wei, D. R. Liu, and H. W. Ma, “Adaptive tracking control of leader-following linear multi-agent systems with external disturbances,” Int. J. Syst. Sci., vol. 47, no. 13, pp. 3167–3179, 2016. doi: 10.1080/00207721.2015.1102358
    [32]
    Y. Z. Lv, Z. K. Li, and Z. S. Duan, “Distributed pi control for consensus of heterogeneous multiagent systems over directed graphs,” IEEE Trans. Syst.,Man,Cybernet.:Syst., vol. 50, no. 4, pp. 1602–1609, Apr. 2020. doi: 10.1109/TSMC.2018.2792472
    [33]
    G. H. Wen, Z. S. Duan, G. R. Chen, and W. W. Yu, “Consensus tracking of multi-agent systems with lipschitz-type node dynamics and switching topologies,” IEEE Trans. Circuits Syst. I:Regular Papers, vol. 61, no. 2, pp. 499–511, Feb. 2014. doi: 10.1109/TCSI.2013.2268091
    [34]
    Z. K. Li, G. H. Wen, Z. S. Duan, and W. Ren, “Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs,” IEEE Trans. Autom. Control, vol. 60, no. 4, pp. 1152–1157, Apr. 2015. doi: 10.1109/TAC.2014.2350391
    [35]
    R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge: Cambridge University Press, 2012.
    [36]
    X. Y. Yu, P. X. Ding, F. Yang, C. Zou, and L. L. Ou, “Stabilization parametric region of distributed PID controllers for general first-order multi-agent systems with time delay,” IEEE/CAA J. Autom. Sinica, pp. 1–10, Jul. 2019.
    [37]
    C. Huang, G. S. Zhai, and G. S. Xu, “Necessary and sufficient conditions for consensus in third order multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1044–1053, Nov. 2018. doi: 10.1109/JAS.2018.7511222
    [38]
    S. Shi, S. Y. Xu, and H. Y. Feng, “Robust fixed-time consensus tracking control of high-order multiple nonholonomic systems,” IEEE Trans. Syst., Man, Cybernet.: Syst., Apr. 2019, DOI: 10.1109/TSMC.2019.2906902.
    [39]
    U. Hassler, “Ito’s lemma,” Stochastic Processes and Calculus, U. Hassler, Ed. Cham, Germany: Springer, 2016, pp. 239–258.
    [40]
    L. Cheng, Y. P. Wang, W. Ren, Z. G. Hou, and M. Tan, “On convergence rate of leader-following consensus of linear multi-agent systems with communication noises,” IEEE Trans. Autom. Control, vol. 61, no. 11, pp. 3586–3592, Nov. 2016. doi: 10.1109/TAC.2016.2522647
    [41]
    S. E. Tuna, “Conditions for synchronizability in arrays of coupled linear systems,” IEEE Trans. Autom. Control, vol. 54, no. 10, pp. 2416–2420, Oct. 2009. doi: 10.1109/TAC.2009.2029296

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(6)

    Article Metrics

    Article views (1339) PDF downloads(145) Cited by()

    Highlights

    • A new distributed control law for multi-agent system is proposed.
    • The system is directed and inferred by external stochastic disturbance.
    • The proposed control law can solve the dynamic consensus problems.

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return