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Exponential synchronization of Markovian jumping complex dynamical networks with randomly occurring parameter uncertainties

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Abstract

This paper investigates the mean-square exponential synchronization problem of complex dynamical networks with Markovian jumping and randomly occurring parameter uncertainties. The considered Markovian transition rates are assumed to be partially unknown. The parameter uncertainties are considered to be random occurrence and norm-bounded, and the randomly occurring parameter uncertainties obey certain Bernoulli-distributed white noise sequences. Based on the Lyapunov method and stochastic analysis, by designing mode-dependent feedback controller, some sufficient conditions are presented to ensure the mean-square exponential synchronization of Markovian jumping complex dynamical networks with partly unknown transition rates and randomly occurring parameter uncertainties. Numerical examples are given to demonstrate the validity of the theoretical results.

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References

  1. Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)

    Article  Google Scholar 

  2. Boccaletti, S., Latora, V., Moreno, Y., Chevez, M., Hwqng, D.U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)

    Article  MathSciNet  Google Scholar 

  3. Chen, Y., Lü, J.H., Yu, X.H., Hill, David J.: Multi-agent systems with dynamical topologies: consensus and applications. IEEE Circuits Syst. Mag. 3, 21–34 (2013)

    Article  Google Scholar 

  4. 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 

  5. Wang, X.F., Chen, G.R.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos 12, 2735–2749 (2012)

    Google Scholar 

  6. Chen, Y., Lü, J.H., Lin, Z.L.: Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica 49, 1768–1775 (2013)

    Article  Google Scholar 

  7. Chen, Y., Lü, J.H., Yu, X.H., Lin, Z.L.: Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices. SIAM J. Control Optim. 51, 3274–3301 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lü, J.H., Chen, G.R.: A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Autom. Control 50, 841–846 (2005)

    Article  Google Scholar 

  9. Zhou, J., Lu, J.A., Lü, J.H.: Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans. Autom. control 51, 652–656 (2006)

    Article  Google Scholar 

  10. Liu, X.W., Chen, T.P.: Cluster synchronization in directed networks via intermittent pinning control. IEEE Trans. Neural Netw. 22, 1009–1020 (2011)

    Article  Google Scholar 

  11. Xia, W.G., Cao, J.D.: Pinning synchronization of delayed dynamical networks via intermittent control. Chaos 19, 013120 (2009)

    Article  MathSciNet  Google Scholar 

  12. Chen, T.P., Liu, X.W., Lu, W.L.: Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I(54), 1317–1326 (2007)

    Article  MathSciNet  Google Scholar 

  13. Feng, J.W., Sun, S.H., Xu, C.: The synchronization of general complex dynamical network via pinning control. Nonlinear Dyn. 67, 1623–1633 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lu, J.Q., Kurths, J., Cao, J., Mahdavi, N., Huang, C.: Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans. Neural Netw. Learn. Syst. 23, 285–292 (2012)

    Article  Google Scholar 

  15. Zhou, J., Wu, Q.J., Xiang, L.: Pinning complex delayed dynamical networks by a single impulsive controller. IEEE Trans. Circuits Syst. I(58), 2882–2893 (2011)

    Article  MathSciNet  Google Scholar 

  16. Li, P., Cao, Jd, Wang, Z.D.: Robust impulsive synchronization of coupled delayed neural networks with uncertainties. Physica A 373, 261–272 (2007)

    Article  Google Scholar 

  17. Xu, Y.H., Yang, H.Z., Tong, D.B., Wang, Y.L.: Adaptive exponential synchronization in pth moment for stochastic time varying multi-delayed complex networks. Nonlinear Dyn. 73, 1423–1431 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tong, D.B., Zhu, Q.Y., Zhou, W.N.: Adaptive synchronization for stochastic T-S fuzzy neural networks with time delay and Markovian jumping parameters. Neurocomputing 117, 91–97 (2013)

    Article  Google Scholar 

  19. Zhou, W.N., Tong, D.B., Gao, Y., Ji, C., Su, H.Y.: Mode and delay-dependent adaptive exponential synchronization in \(p\)th moment for stochastic delayed neural networks with Markovian switching. IEEE Trans. Neural Netw. Learn. Syst. 4, 662–668 (2012)

  20. Shen, B., Wang, Z.D., Liu, X.H.: Sampled-data synchronization control of dynamical networks with stochastic sampling. IEEE Trans. Autom. Control 57, 2644–2650 (2012)

    Article  MathSciNet  Google Scholar 

  21. Lee, T.H., Park, J.H., Lee, S.M., Kwon, O.M.: Robust synchronization of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control. Int. J. Control 86, 107–119 (2013)

  22. Li, Z., Chen, G.R.: Global synchronization and asymptotic stability of complex dynamical networks. IEEE Trans. Circuits Syst. II(53), 28–33 (2006)

    Google Scholar 

  23. Tang, Y., Wong, W.K.: Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Trans. Neural Netw. Learn. Syst. 24, 435–447 (2013)

    Article  Google Scholar 

  24. 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)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yuan, K.: Robust synchronization in arrays of coupled networks with delay and mixed coupling. Neurocomputing 72, 1026–1031 (2009)

    Article  Google Scholar 

  26. Wang, T.B., Zhou, W.N., Zhao, S.W.: Robust synchronization for stochastic delayed complex networks with switching topology and unmodeled dynamics via adaptive control approach. Commun. Nonlinear Sci. Numer. Simulat. 18, 2097–2106 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hu, J., Wang, Z.D., Gao, H.J., Stergioulas, L.K.: Robust sliding mode control for discrete stochastic systems with mixed time-delays, randomly occurring uncertainties and nonlinearities. IEEE Trans. Ind. Electron. 59, 3008–3015 (2012)

    Article  Google Scholar 

  28. Liu, Y.R., Wang, Z.D., Liu, X.H.: Exponential synchronization of complex networks with Markovian jump and mixed delays. Phys. Lett. A 372, 3986–3998 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhu, Q.X., Cao, J.D.: Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays. IEEE Trans. Syst. Man Cybern. 41, 341–353 (2011)

    Google Scholar 

  30. Ma, Q., Xu, S.Y., Zou, Y.: Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities. Neurocomputing 74, 3404–3411 (2011)

    Article  Google Scholar 

  31. Lu, Y., Ren, W., Yi, S., Zou, Y.: Stability analysis for discrete delayed Markovian jumping neural networks with partly unknown transition probabilities. Neurocomputing 74, 3768–3772 (2011)

    Article  Google Scholar 

  32. Kang, Y., Zhang, J.F., Ge, S.S.: Robust output feedback H infinity control of uncertain Markovian jump systems with mode-dependent time-delays. Int. J. Control 81, 43–61 (2008)

  33. Lin, Z.W., Lin, Y., Zhang, W.H.: A unified design for state and output feedback H infinity control of nonlinear stochastic Markovian jump systems with state and disturbance-dependent noise. Automatica 54, 2955–2962 (2009)

    Article  Google Scholar 

  34. Mao, X.R., Yuan, C.G.: Stochastic Differential Equations with Markovian Switching. Imperial College Press, London, London (2006)

    Book  MATH  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (61203337), the Innovation Program of Shanghai Municipal Education Commission (12zz064), the Specialized Research Fund for the Doctoral Program of Higher Education (20120075120009), and the Natural Science Foundation of Shanghai (12Z R1440200).

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Authors and Affiliations

  1. College of Computer Sciences and Technology, Donghua University, Shanghai,  201620, China

    Wuneng Zhou, Anding Dai, Jun Yang & Huashan Liu

  2. School of Electronic Engineering, Dongguan University of Technology, Dongguan,  523808, China

    Xueliang Liu

  3. Engineering Research Center of Digitized Textile & Fashion Technology, Ministry of Education, Donghua University, Shanghai,  201620, China

    Wuneng Zhou

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  1. Wuneng Zhou
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  2. Anding Dai
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  3. Jun Yang
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  4. Huashan Liu
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Correspondence to Wuneng Zhou or Anding Dai.

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Zhou, W., Dai, A., Yang, J. et al. Exponential synchronization of Markovian jumping complex dynamical networks with randomly occurring parameter uncertainties. Nonlinear Dyn 78, 15–27 (2014). https://doi.org/10.1007/s11071-014-1418-x

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