Nonlinear Dynamics

, Volume 95, Issue 2, pp 1713–1730 | Cite as

Cluster-delay consensus in MASs with layered intermittent communication: a multi-tracking approach

  • Da Huang
  • Haijun JiangEmail author
  • Zhiyong Yu
  • Cheng Hu
  • Xiaolin Fan


In this paper, a class of cluster consensus problem of the multi-agent systems with aperiodic intermittent communication is studied through tracking approach. Due to the transmission ways of information in the network, a new notion of layered intermittence is developed. To track the leading subnetwork and reach the desired consensus, a new type of pinning-like consensus protocol with aperiodic intermittent effects is designed according to the topological properties of agents. Considering both the control protocol with intermittent effects and the intermittent communication, the protocol is applied to construct several new intermittent switching systems. Besides, the graph of the networked system is assumed to be directed and weakly connected. Some consensus criteria are derived to guarantee that the agents in the same cluster follow the leader asymptotically, while agents in different clusters reach the desired delay consensus via tracking their leaders. Finally, some numerical simulations are given to illustrate the effectiveness of the theoretical results.


Clustered network Multi-agent system Leader-following Cluster consensus Intermittent communication 



We express our sincere gratitude to the people who gave us valuable comments. This work was supported by National Natural Science Foundation of Peoples Republic of China (NSFC) (Grants Nos. 61473244, 11402223), the National Natural Science Foundation of Xinjiang (NSFXJ) (No. 2015211B005) and NSFC No. 11661077, the Scientific Research program of the Higher Education Institution of Xinjiang (grant no. XJEDU2017T001), the Excellent Young Talents in Science and Technology Project of Xinjiang (grant no. 2017Q032), Education Program of Xinjiang Tianshan Talents (No. 2018xgytsyc2-5).


  1. 1.
    Saber, O., Murray, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49, 1520–1533 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ma, Z.J., Wang, Y., Li, X.M.: Cluster-delay consensus in first-order multi-agent systems with nonlinear dynamics. Nolinear Dyn. 83, 1303–1310 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Wen, G.H., Duan, Z.S., Ren, W., Chen, G.R.: Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications. Int. J. Robust Nonlinear Control 24, 2438–2457 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Liao, X.F., Ji, L.H.: On pinning group consensus for dynamical multi-agent networks with general connected topology. Neurocomputing 135, 262–267 (2014)CrossRefGoogle Scholar
  5. 5.
    Qin, J.H., Yu, C.B.: Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition. Automatica 49, 2898–2905 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Yu, J.Y., Wang, L.: Group consensus of multi-agent systems with directed information exchange. Int. J. Syst. Sci. 43, 334–348 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chen, F., Chen, Z.Q., Xiang, L.Y., Liu, Z.X., Yuan, Z.Z.: Reaching a consensus via pinning control. Automatica 45, 1215–1220 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Huang, N., Duan, Z.S., Zhao, Y.: Leader-following consensus of second-order non-linear multi-agent systems with directed intermittent communication. IET Control Theory Appl. 8, 782–795 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ma, Q., Wang, Z., Miao, G.Y.: Second-order group consensus for multi-agent systems via pinning leader-following approach. J. Frankl. Inst. 351, 1288–1300 (2014)CrossRefzbMATHGoogle Scholar
  10. 10.
    Yu, Z.Y., Jiang, H.J., Hu, C., Fan, X.L.: Consensus of second-order multi-agent systems with delayed nonlinear dynamics and aperiodically intermittent communications. Int. J. Control 90(5), 909–922 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Li, H.J.: Leader-following consensus of nonlinear multi-agent systems with mixed delays and uncertain parameters via adaptive pinning intermittent control. Nonlinear Anal. Hybrid Syst. 22, 202–214 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Cui, Q., Xie, D.M., Jiang, F.C.: Group consensus tracking control of second-order multi-agent systems with directed fixed topology. Neurocomputing 218, 286–295 (2016)CrossRefGoogle Scholar
  13. 13.
    Zheng, Y., Zhu, Y., Wang, L.: Consensus of heterogeneous multi-agent systems. IET Control Theory Appl. 5, 1881–1888 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Wen, G.H., Duan, Z.S., Yu, W.W., Chen, G.R.: Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications. Int. J. Control 86, 322–331 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Wang, G., Shen, Y.: Second-order cluster consensus of multi-agent dynamical systems with impulsive effects. Commun. Nonlinear Sci. Numer. Simul. 19, 3220–3228 (2014)MathSciNetCrossRefGoogle Scholar
  16. 16.
    You, X., Hua, C.C., Guan, X.P.: Event-triggered leader-following consensus for nonlinear multi-agent systems subject to actuator saturation using dynamic output feedback method. Autom. Control, IEEE Trans (2018). zbMATHGoogle Scholar
  17. 17.
    You, X., Hua, C.C., Guan, X.P.: Self-triggered Leader-following consensus for high-order nonlinear multiagent systems via dynamic output feedback control. IEEE Trans. Cybern.
  18. 18.
    Hua, C.C., You, X., Guan, X.P.: Leader-following consensus for a class of high-order nonlinear multi-agent systems short communication. Automatica 73, 138–144 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Hu, C., Jiang, H.J.: Pinning synchronization for directed networks with node balance via adaptive intermittent control. Nonlinear Dyn. 80, 295–307 (2015)CrossRefzbMATHGoogle Scholar
  20. 20.
    Ma, Q., Lu, J.W.: Cluster synchronization for directed complex dynamical networks via pinning control. Neurocomputing 101, 354–360 (2013)CrossRefGoogle Scholar
  21. 21.
    Wu, Z.Y., Fu, X.C.: Cluster mixed synchronization via pinning control and adaptive coupling strength in community networks with nonidentical nodes. Commun. Nonlinear Sci. Numer. Simul. 17(4), 1628–1636 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Wang, G., Shen, Y.: Cluster synchronisation of directed complex dynamical networks with nonidentical nodes via pinning control. Int. J. Syst. Sci. 44, 1577–1586 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Yu, C.B., Qin, J.H., Gao, H.J.: Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control. Automatica 50, 2341–2349 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Wu, Z.Y., Fu, X.C.: Cluster lag synchronisation in community networks via linear pinning control with local intermittent effect. Phys. A 395, 487–498 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Nian, F.Z., Wang, X.Y.: Optimal pinning synchronization on directed complex network. Chaos 21, 043131 (2011)CrossRefzbMATHGoogle Scholar
  26. 26.
    Sun, W.G., Wang, S., Wang, G.H., Wu, Y.Q.: Lag synchronization via pinning control between two coupled networks. Nonlinear Dyn. 79, 2659–2666 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Wu, X.Q., Zheng, W.X., Zhou, J.: Generalized outer synchronization between complex dynamical networks. Chaos 19, 013109 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Yu, W.W., Chen, G.R., Lü, J.H.: On pinning synchronization of complex dynamical networks. Automatica 45, 429–435 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Hu, C., Yu, J., Jiang, H.J., Teng, Z.D.: Pinning synchronization of weighted complex networks with variable delays and adaptive coupling weights. Nonlinear Dyn. 67(2), 1373–1385 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Lu, R.Q., Yu, W.W., Lü, J.H., Xue, A.K.: Synchronization on complex networks of networks. IEEE Trans. Neural Netw. Learn. Syst. 25, 2110–2118 (2014)CrossRefGoogle Scholar
  31. 31.
    Song, Q., Cao, J.D.: On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans. Circuits Syst. I Regul. Pap. 57, 672–680 (2010)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Feng, J.W., Sun, S.H., Xu, C., Zhao, Y., Wang, J.Y.: The synchronization of general complex dynamical network via pinning control. Nonlinear Dyn. 67(2), 1623–1633 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Wang, J.Y., Feng, J.W., Xu, C., Zhao, Y.: Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix. Nonlinear Dyn. 67, 1635–1646 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Wu, W., Zhou, W.J., Chen, T.P.: Cluster synchronization of linearly coupled complex networks under pinning control. IEEE Trans. Circuits Syst. I(56), 829–839 (2009)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Lu, X.B., Qin, B.Z.: Adaptive cluster synchronization in complex dynamical networks. Phys. Lett. A 373, 3650–3658 (2009)CrossRefzbMATHGoogle Scholar
  36. 36.
    Liu, X.W., Chen, T.P.: Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control. IEEE Trans. Neural New. Learn. Syst. 26(10), 2396–2407 (2015)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Wu, Z.Y., Xu, X.J., Chen, G.R., Fu, X.C.: Adaptive synchronization and pinning control of colored networks. Chaos 22, 043137 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Bondy, J., Murty, U.: Graph Theory. Springer, New York (2008)CrossRefzbMATHGoogle Scholar
  39. 39.
    Horn, R., Johnson, C.: Matrix Analysis, 2nd edn. Cambridge University Press, Cambridge (2013)zbMATHGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of Mathematics and System SciencesXinjiang UniversityUrumqiChina
  2. 2.Xinjiang Institute of EngineeringUrumqiChina

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