Journal of Systems Science and Complexity

, Volume 30, Issue 5, pp 1042–1060 | Cite as

Output consensus for heterogeneous nonlinear multi-agent systems based on T-S fuzzy model

  • Xiaolei Li
  • Xiaoyuan LuoEmail author
  • Shaobao Li
  • Xinping Guan


In this paper, the output consensus problem of general heterogeneous nonlinear multi-agent systems subject to different disturbances is considered. A kind of Takagi-Sukeno fuzzy modeling method is used to describe the nonlinear agents’ dynamics. Based on the model, a distributed fuzzy observer and controller are designed based on parallel distributed compensation scheme and internal reference models such that the heterogeneous nonlinear multi-agent systems can achieve output consensus. Then a necessary and sufficient condition is presented for the output consensus problem. And it is shown that the consensus trajectory of the global fuzzy model is determined by the network topology and the initial states of the internal reference models. Finally, some simulations are given to illustrate and verify the effectiveness of the proposed scheme.


Heterogeneous nonlinear multi-agent system internal reference model output consensus T-S fuzzy model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Kuriki Y and Namerikawa T, Consensus-based cooperative formation control with collision avoidance for a multi-UAV system, 2014 American Control Conference, 2014, 2077–2082.CrossRefGoogle Scholar
  2. [2]
    Zuo Z Q, Zhang J, and Wang Y J, Adaptive fault-tolerant tracking control for linear and lipschitz nonlinear multi-agent systems, IEEE Transactions on Industrial Electronics, 2015, 62(6): 3923–3931.Google Scholar
  3. [3]
    Su H S, Wang X F, and Lin Z L, Flocking of multi-agents with a virtual leader, IEEE Trans. Autom. Control, 2009, 54(2): 293–307.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Lin Z Y, Wang L, Han Z, et al., Distributed formation control of multi-agent systems using complex Laplacian, IEEE Trans. Autom. Control, 59(7): 1765–1777.Google Scholar
  5. [5]
    Zhu S, Chen C L, Li W, et al., Distributed optimal consensus filter for target tracking in heterogeneous sensor networks, IEEE Trans. Cybernetics, 2013, 43(6): 1963–1976.CrossRefGoogle Scholar
  6. [6]
    Olfati-Saber R and Murray R, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Autom. Control, 2004, 49(9): 1520–1533.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Yu W W, Ren W, Zheng W, et al., Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics, Automatica, 2013, 49(7): 2107–2115.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Wang J K, Fu J K, and Zhang G S, Finite-time consensus problem for multiple non-holonomic agents with communication delay, Journal of Systems Science and Complexity, 2015, 28(3): 559–569.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    You K Y and Xie L H, Network topology and communication data rate for consensusability of discrete-time multi-agent systems, IEEE Trans. Autom. Control, 2011, 56(10): 1520–1533.MathSciNetGoogle Scholar
  10. [10]
    You K Y and Xie L H, Consensusability of discrete-time multi-agent systems over directed graphs, Proc. 30th Chinese Control Conference, Yantai, China, 2011, 6413–6418.Google Scholar
  11. [11]
    Hua C C, Yang Y N, and Liu P, Output-feedback adaptive control of networked teleoperation system with time-varying delay and bounded inputs, IEEE/ASME Transactions on Mechatronics, 2015, 20(5): 2009–2020.CrossRefGoogle Scholar
  12. [12]
    Yang X, Luo H, Krueger M, et al., Online monitoring system design for roll eccentricity in rolling mills, IEEE Transactions on Industrial Electronics, 2016, 63(4): 2559–2568.CrossRefGoogle Scholar
  13. [13]
    Xi J, Shi Z, and Zhong Y, Output consensus analysis and design for high-order linear swarm systems: Partial stability method, Automatica, 2012, 48(9): 2335–2343.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Zhang H, Feng H, Yan H, et al., Observer-based output feedback event-triggered control for consensus of multi-agent systems, IEEE Trans. Industrial Electronics, 2014, 61(9): 4885–4893.CrossRefGoogle Scholar
  15. [15]
    Wang J H, Liu Z X, Hu X M, Consensus control design for multi-agent systems using relative output feedback, Journal of Systems Science and Complexity, 2014, 27(2): 237–251.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Xiong X, Yu W, Lü J, et al., Fuzzy modelling and consensus of nonlinear multi-agent systems with variable structure, IEEE Trans. Circuits Syst. I, Reg. Papers, 2014, 61(4): 1183–1191.CrossRefGoogle Scholar
  17. [17]
    Zhao Y, Li B, Qin J, et al., H consensus and synchronization of nonlinear systems based on a novel fuzzy model, IEEE Trans. Cybern., 2013, 43(6): 2157–2169.CrossRefGoogle Scholar
  18. [18]
    Kim H, Shim H, and Seo J H, Output consensus of heterogeneous uncertain linear multi-agent systems, IEEE Trans. Autom. Control, 2011, 56(1): 200–206.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Li S B, Feng G, Luo X Y, et al., Output consensus of heterogeneous linear discrete-time multi-agent systems with structural uncertainties, IEEE Trans. Cybernetics, 2015, 45(12): 2868–2879.CrossRefGoogle Scholar
  20. [20]
    Li S B, Feng G, Luo X Y, et al., Output consensus of heterogeneous linear multi-agent systems subject to different disturbances, Asian Journal of Control, 2016, 18(2): 757–762.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Godsil C and Royle G, Algebraic Graph Theory, Springer Verlag, New York, 2001.CrossRefzbMATHGoogle Scholar
  22. [22]
    Lin P, Jia Y, and Li L, Distributed robust H consensus control in directed networks of agents with time delay, Systems & Control Letters, 2008, 57(8): 643–653.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Mohar B, Eigenvalues, diameter, and mean distance in graphs, Graphs and Combinatories, 1991, 7(1): 53–64.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Meda-Campaña J A, Gómez-Mancilla J C, and Castillo-Toledo B, Exact output regulation for nonlinear systems described by Takagi–Sugeno fuzzy models, IEEE Trans. Fuzzy Syst., 2012, 20(2): 235–247.CrossRefGoogle Scholar
  25. [25]
    Meda-Campaña J A, Castillo-Toledo B, and Zúñiga V, On the nonlinear fuzzy regulation for under-actuated systems, Proc. IEEE Int. Conf. Fuzzy Syst., Vancouver, BC, Canada, Jul. 16–21, 2006, 2195–2202.Google Scholar
  26. [26]
    Su Y F and Huang J, Cooperative output regulation with application to multi-agent consensus under switching network, IEEE Trans. Systems, Man, and Cybern., Part B, 2012, 42(3): 864–875.CrossRefGoogle Scholar
  27. [27]
    Huang J, Nolinear Output Regulation: Theory and Applications, SIAM, Phildelphia, 2004.CrossRefGoogle Scholar
  28. [28]
    Li Z, Duan Z S, Chen G R, et al., Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint, IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, 2010, 57(1): 213–224.MathSciNetGoogle Scholar
  29. [29]
    He W and Ge S, Robust adaptive boundary control of a vibrating string under unknown timevarying disturbance, IEEE Trans. Control Syst. Tech., 2012, 20(1): 48–58.Google Scholar
  30. [30]
    Yang Z, Fukushima Y, and Qin P, Decentralized adaptive robust control of robot manipulators using disturbance observers, IEEE Trans. Control Syst. Tech., 2012, 20(5): 1357–1365.CrossRefGoogle Scholar
  31. [31]
    Tuna S E, LQR-based coupling gain for synchronization of linear systems, Available: /0801.3390.Google Scholar
  32. [32]
    Li Z, Ren W, Liu X, et al., Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols, IEEE Trans. Autom. Control, 2013, 58(7): 1786–1791.MathSciNetCrossRefGoogle Scholar
  33. [33]
    Li Z, Ren W, Liu X, et al., Distributed consensus of linear multi-agent systems with adaptive dynamic protocols, Automatica, 2013, 49(7): 1986–1995.MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    Ma X and Sun Z, Output tracking and regulation of nonlinear system based on Takagi-Sugeno fuzzy model, IEEE Trans. Systems, Man, and Cybern., Part B, 2000, 30(1): 47–59.CrossRefGoogle Scholar
  35. [35]
    Misra V, Gong W, and Towsley D, Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED, Proceeding of ACM/SIGCOMM, Sweden, 2000, 151–160.Google Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Xiaolei Li
    • 1
  • Xiaoyuan Luo
    • 1
    • 2
    Email author
  • Shaobao Li
    • 1
  • Xinping Guan
    • 3
  1. 1.School of Electrical EngineeringYanshan UniversityQinhuangdaoChina
  2. 2.Polytechnic School of EngineeringNew York UniversityNew YorkUSA
  3. 3.Institute of Electronic, Information and Electrical EngineeringShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations