Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  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. Cao, J.D., Lu, J.Q.: Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16, 013133-1–013133-6 (2006)

    MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  5. Wang, X.F.: Complex networks: topology, dynamics and synchronization. Int. J. Bifurc. Chaos 12, 885–916 (2002)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  8. Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82, 3042–3045 (1999)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    MathSciNet  Google Scholar 

  12. Motter, A.E., Zhou, C.S., Kurths, J.: Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E 71, 016116 (2005)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  15. Zhou, C.S., Motter, A.E., Kurths, J.: Universality in the synchronization of weighted random networks. Phys. Rev. Lett. 96, 034101 (2006)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  17. Zhou, C.S., Kurths, J.: Dynamical weights and enhanced synchronization in adaptive complex networks. Phys. Rev. Lett. 96, 164102 (2006)

    Article  Google Scholar 

  18. Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.S.: Synchronization in complex networks. Phys. Rep. 469, 93–153 (2008)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  23. Wang, X.F., Chen, G.R.: Pinning control of scale-free dynamical networks. Phys. A 310, 521–531 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. Żochowski, M.: Intermittent dynamical control. Phys. D Nonlinear Phenom. 145, 181–190 (2000)

    Article  MATH  Google Scholar 

  25. Drakunov, S.V., Utkin, V.I.: Sliding mode control in dynamic systems. Int. J. Control 55, 1029–1037 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  35. Zheng, S.: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dyn. 74, 957–967 (2013)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  39. Shao, Y.F., Zhang, Q.H.: Stability and periodicity for impulsive neural networks with delays. Adv. Differ. Equ. 2013, 352 (2013)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

Download references

Acknowledgments

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).

Author information

Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Hui Zhao, Jinghua Xiao & Mingwen Zheng

  2. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Lixiang Li, Haipeng Peng & Yixian Yang

Authors
  1. Hui Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lixiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haipeng Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinghua Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yixian Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mingwen Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lixiang Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, H., Li, L., Peng, H. et al. Impulsive control for synchronization and parameters identification of uncertain multi-links complex network. Nonlinear Dyn 83, 1437–1451 (2016). https://doi.org/10.1007/s11071-015-2416-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2416-3

Keywords

Search

Navigation