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.
Similar content being viewed by others
References
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)
Cao, J.D., Lu, J.Q.: Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16, 013133-1–013133-6 (2006)
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)
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)
Wang, X.F.: Complex networks: topology, dynamics and synchronization. Int. J. Bifurc. Chaos 12, 885–916 (2002)
Chen, L., Lu, J.A.: Cluster synchronization in a complex dynamical network with two nonidentical clusters. J. Syst. Sci. Complex. 21, 20–33 (2008)
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)
Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82, 3042–3045 (1999)
Chen, S., Cao, J.D.: Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch. Nonlinear Dyn. 67, 1397–1406 (2012)
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)
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)
Motter, A.E., Zhou, C.S., Kurths, J.: Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E 71, 016116 (2005)
Li, X., Chen, G.R.: Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint. IEEE Trans. Circuits Syst. I 50, 1381–1390 (2003)
Wang, X.F., Chen, G.R.: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circuits Syst. I 49, 54–62 (2002)
Zhou, C.S., Motter, A.E., Kurths, J.: Universality in the synchronization of weighted random networks. Phys. Rev. Lett. 96, 034101 (2006)
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)
Zhou, C.S., Kurths, J.: Dynamical weights and enhanced synchronization in adaptive complex networks. Phys. Rev. Lett. 96, 164102 (2006)
Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.S.: Synchronization in complex networks. Phys. Rep. 469, 93–153 (2008)
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)
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)
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)
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)
Wang, X.F., Chen, G.R.: Pinning control of scale-free dynamical networks. Phys. A 310, 521–531 (2002)
Żochowski, M.: Intermittent dynamical control. Phys. D Nonlinear Phenom. 145, 181–190 (2000)
Drakunov, S.V., Utkin, V.I.: Sliding mode control in dynamic systems. Int. J. Control 55, 1029–1037 (1992)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Zheng, S.: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dyn. 74, 957–967 (2013)
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)
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)
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)
Shao, Y.F., Zhang, Q.H.: Stability and periodicity for impulsive neural networks with delays. Adv. Differ. Equ. 2013, 352 (2013)
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)
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)
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)
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)
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
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-015-2416-3