Nonlinear Dynamics

, Volume 83, Issue 3, pp 1437–1451 | Cite as

Impulsive control for synchronization and parameters identification of uncertain multi-links complex network

  • Hui Zhao
  • Lixiang Li
  • Haipeng Peng
  • Jinghua Xiao
  • Yixian Yang
  • Mingwen Zheng
Original Paper


In this paper, the exponential and finite-time synchronization and parameters identification for uncertain multi-links complex network are investigated by using the impulsive control method. It is known that impulsive control, as an effective and ideal control technique, can not only realize the synchronization goal but also reduce the control cost. The paper proposes an impulsive complex network model with uncertain parameter. Two different kinds of adaptive feedback controllers are further designed based on impulsive delay differential inequalities, and the purpose is to achieve the exponential synchronization, finite-time synchronization and obtain parameters identification simultaneously. Several novel and useful exponential and finite-time synchronization criteria are also derived based on global exponential stability theory and finite-time stability theory. Finally, two numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.


Finite-time control theory Multi-links complex network Parameters identification Impulsive control method 



The authors thank all the Editor and the anonymous referees for their constructive comments and valuable suggestions, which are helpful to improve the quality of this paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 61472045, 61573067), the Scientific Research Project of Beijing Municipal Commission of Education (Grant Nos. KZ201 50015015, KM201510015009), and the Beijing Natural Science Foundation (Grant No. 4142016).


  1. 1.
    Zhao, H., Li, L.X., Peng, H.P., Xiao, J.H., Yang, Y.X.: Mean square modified function projective synchronization of uncertain complex network with multi-links and stochastic perturbations. Eur. Phys. J. B 88, 1–8 (2015)Google Scholar
  2. 2.
    Cao, J.D., Lu, J.Q.: Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16, 013133-1–013133-6 (2006)MathSciNetGoogle Scholar
  3. 3.
    Qin, H.X., Ma, J., Jin, W.Y., Wang, ChN: Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci. China Technol. Sci. 57, 936–946 (2014)CrossRefGoogle Scholar
  4. 4.
    Ma, J., Qin, H.X., Song, X.L.: Pattern selection in neuronal network driven by electric autapses with diversity in time delays. Int. J. Mod. Phys. B 29, 1450239 (2015)CrossRefGoogle Scholar
  5. 5.
    Wang, X.F.: Complex networks: topology, dynamics and synchronization. Int. J. Bifurc. Chaos 12, 885–916 (2002)CrossRefzbMATHGoogle Scholar
  6. 6.
    Chen, L., Lu, J.A.: Cluster synchronization in a complex dynamical network with two nonidentical clusters. J. Syst. Sci. Complex. 21, 20–33 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    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
  8. 8.
    Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82, 3042–3045 (1999)CrossRefGoogle Scholar
  9. 9.
    Chen, S., Cao, J.D.: Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch. Nonlinear Dyn. 67, 1397–1406 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Cao, J.D., Wang, Z.D., Sun, Y.H.: Synchronization in an array of linearly stochastically coupled networks with time delays. Phys. A 385, 718–728 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zhao, H., Li, L.X., Peng, H.P., Kurths, J., Xiao, J.H., Yang, Y.X.: Anti-synchronization for stochastic memristor-based neural networks with non-modeled dynamics via adaptive control approach. Eur. Phys. J. B 88, 1–10 (2015)MathSciNetGoogle Scholar
  12. 12.
    Motter, A.E., Zhou, C.S., Kurths, J.: Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E 71, 016116 (2005)CrossRefGoogle Scholar
  13. 13.
    Li, X., Chen, G.R.: Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint. IEEE Trans. Circuits Syst. I 50, 1381–1390 (2003)CrossRefGoogle Scholar
  14. 14.
    Wang, X.F., Chen, G.R.: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circuits Syst. I 49, 54–62 (2002)CrossRefGoogle Scholar
  15. 15.
    Zhou, C.S., Motter, A.E., Kurths, J.: Universality in the synchronization of weighted random networks. Phys. Rev. Lett. 96, 034101 (2006)CrossRefGoogle Scholar
  16. 16.
    Anbuvithya, R., Mathiyalagan, K., Sakthivel, R., Prakasha, P.: Non-fragile synchronization of memristive BAM networks with random feedback gain fluctuations. Commun. Nonlinear Sci. Numer. Simul. 29, 427–440 (2015)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhou, C.S., Kurths, J.: Dynamical weights and enhanced synchronization in adaptive complex networks. Phys. Rev. Lett. 96, 164102 (2006)CrossRefGoogle Scholar
  18. 18.
    Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.S.: Synchronization in complex networks. Phys. Rep. 469, 93–153 (2008)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Yang, T., Chua, L.O.: Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 44, 976–988 (1997)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Liu, B., Liu, X.Z., Chen, G.R., Wang, H.Y.: Robust impulsive synchronization of uncertain dynamical networks. IEEE Trans. Circuits Syst. I 52, 1431–1441 (2005)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Mathiyalagan, K., Park, J.H., Sakthivel, R.: Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities. Appl. Math. Comput. 259, 967–979 (2015)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Li, X., Wang, X.F., Chen, G.R.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circuits Syst. I 51, 2074–2087 (2004)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wang, X.F., Chen, G.R.: Pinning control of scale-free dynamical networks. Phys. A 310, 521–531 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Żochowski, M.: Intermittent dynamical control. Phys. D Nonlinear Phenom. 145, 181–190 (2000)CrossRefzbMATHGoogle Scholar
  25. 25.
    Drakunov, S.V., Utkin, V.I.: Sliding mode control in dynamic systems. Int. J. Control 55, 1029–1037 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Sakthivel, R., Samidurai, R., Anthoni, S.M.: Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects. J. Optim. Theory Appl. 147, 583–596 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Sakthivel, R., Raja, R., Anthoni, S.M.: Exponential stability for delayed stochastic bidirectional associative memory neural networks with markovian jumping and impulses. J. Optim. Theory Appl. 150, 166–187 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Wang, X., Fang, J.A., Mao, H.Y., Dai, A.D.: Finite-time global synchronization for a class of Markovian jump complex networks with partially unknown transition rates under feedback control. Nonlinear Dyn. 79, 47–61 (2015)CrossRefGoogle Scholar
  29. 29.
    Mei, J., Jiang, M.H., Wang, X.H., Han, J.L., Wang, ShT: Finite-time synchronization of drive-response systems via periodically intermittent adaptive control. J. Frankl. Inst. 351, 2691–2710 (2014)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Cui, W.X., Sun, S.Y., Fang, J.A., Xu, Y.L., Zhao, L.D.: Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates. J. Frankl. Inst. 351, 2543–2561 (2014)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Li, L.X., Kurths, J., Peng, H.P., Yang, Y.X., Luo, Q.: Exponentially asymptotic synchronization of uncertain complex time-delay dynamical networks. Eur. Phys. J. B 86, 1–9 (2013)Google Scholar
  32. 32.
    Xiao, J., Zeng, Z.G.: Robust exponential stabilization of uncertain complex switched networks with time-varying delays. Circuits Syst. Signal Process. 33, 1135–1151 (2014)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Wang, T., Zhao, ShW, Zhou, W.N., Yu, W.Q.: Finite-time master–slave synchronization and parameter identification for uncertain Lurie systems. ISA Trans. 53, 1184–1190 (2014)CrossRefGoogle Scholar
  34. 34.
    Mei, J., Jiang, M.H., Wang, B., Long, B.: Finite-time parameter identification and adaptive synchronization between two chaotic neural networks. J. Frankl. Inst. 350, 1617–1633 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Zheng, S.: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dyn. 74, 957–967 (2013)CrossRefzbMATHGoogle Scholar
  36. 36.
    Zhang, Q.J., Luo, J., Wan, L.: Parameter identification and synchronization of uncertain general complex networks via adaptive-impulsive control. Nonlinear Dyn. 75, 353–359 (2013)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Zhang, Q.J., Luo, J., Wan, L.: Erratum to: Parameter identification and synchronization of uncertain general complex networks via adaptive-impulsive control. Nonlinear Dyn. 75, 403–405 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Mei, J., Jiang, M.H., Xu, W.M., Wang, B.: Finite-time synchronization control of complex dynamical networks with time delay. Commun. Nonlinear Sci. Numer. Simul. 18, 2462–2478 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Shao, Y.F., Zhang, Q.H.: Stability and periodicity for impulsive neural networks with delays. Adv. Differ. Equ. 2013, 352 (2013)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Lu, J.Q., Kurths, J., Cao, J.D., Mahdavi, N., Huang, C.: Synchronization Control for Nonliear Stochastic Dynamical Networks: pinning impulsive strategy. IEEE Tans. Neural Netw. Learn. Syst. 23, 285–292 (2012)CrossRefGoogle Scholar
  41. 41.
    Liu, H., Lu, J.Q., Lü, J.H., Hill, D.J.: Structure identification of uncertain general complex dynamical networks with time delay. Automatica 45, 1799–1807 (2009)CrossRefzbMATHGoogle Scholar
  42. 42.
    Si, G.Q., Sun, Z.Y., Zhang, H.Y., Zhang, Y.B.: Parameter estimation and topology identification of uncertain fractional order complex networks. Commun. Nonlinear Sci. Numer. Simul. 17, 5158–5171 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Yang, X.S., Cao, J.D., Ho, D.W.: Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control. Cogn. Neurodyn. 9, 113–128 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Hui Zhao
    • 1
  • Lixiang Li
    • 2
  • Haipeng Peng
    • 2
  • Jinghua Xiao
    • 1
  • Yixian Yang
    • 2
  • Mingwen Zheng
    • 1
  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.Information Security Center, State Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina

Personalised recommendations