Asymptotical synchronization for delayed stochastic neural networks with uncertainty via adaptive control

  • Dongbing Tong
  • Liping Zhang
  • Wuneng Zhou
  • Jun Zhou
  • Yuhua Xu


In this paper, the problem of the adaptive synchronization control is considered for neural networks with uncertainty and stochastic noise. Via utilizing stochastic analysis method and linear matrix inequality (LMI) approach, several sufficient conditions to ensure the adaptive synchronization for neural networks are derived. By the adaptive feedback methods, some suitable parameters update laws are found. Finally, a simulation result is provided to substantiate the effectiveness of the proposed approach.


Neural networks stochastic noises synchronization control time-delays uncertainty 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    W. Feng, S. X. Yang, and H. Wu, “Further results on robust stability of bidirectional associative memory neural networks with norm-bounded uncertainties,” Neurocomputing, vol. 148, pp. 535–543, 2015. [click]CrossRefGoogle Scholar
  2. [2]
    N. Kasabov, K. Dhoble, N. Nuntalid, and G. Indiveri, “Dynamic evolving spiking neural networks for on-line spatioand spectro-temporal pattern recognition,” Neural Netw., vol. 41, pp. 188–201, 2013. [click]CrossRefGoogle Scholar
  3. [3]
    X. Liu, S. Zhong, and X. Ding, “Robust exponential stability of impulsive switched systems with switching delays: a razumikhin approach,” Commun. Nonlinear Sci. Numer. Simulat., vol. 17, no. 4, pp. 1805–1812, 2012. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Z. Wang and H. Zhang, “Global asymptotic stability of reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays,” IEEE Trans. Neural Netw., vol. 21, no. 1, pp. 39–49, 2010. [click]CrossRefGoogle Scholar
  5. [5]
    P. Balasubramaniam, S. Lakshmanan, and R. Rakkiyappan, “LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties,” Int. J. Appl. Math. Comput. Sci., vol. 22, no. 2, pp. 339–351, 2012. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    W. Zhou, D. Tong, Y. Gao, C. Ji, and H. Su, “Mode and delay-dependent adaptive exponential synchronization in pth moment for stochastic delayed neural networks with Markovian switching,” IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 4, pp. 662–668, 2012. [click]CrossRefGoogle Scholar
  7. [7]
    Z.-G. Wu, P. Shi, H. Su, and J. Chu, “Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling,” IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 9, pp. 1368–1376, 2012. [click]CrossRefGoogle Scholar
  8. [8]
    D. Tong, W. Zhou, and H. Wang, “Exponential state estimation for stochastic complex dynamical networks with multi-delayed base on adaptive control,” Int J. Control Autom. Syst., vol. 12, no. 5, pp. 963–968, 2014. [click]CrossRefGoogle Scholar
  9. [9]
    H. Li, “Sampled-data state estimation for complex dynamical networks with time-varying delay and stochastic sampling.” Neurocomputing, vol. 138, pp. 78–85, 2014. [click]CrossRefGoogle Scholar
  10. [10]
    Q. Zhu and J. Cao, “Adaptive synchronization under almost every initial data for stochastic neural networks with timevarying delays and distributed delays,” Commun. Nonlinear Sci. Numer. Simulat. vol. 16, no. 4, pp. 2139–2159, 2011. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    W. Yu, J. Cao, and W. Lu, “Synchronization control of switched linearly coupled neural networks with delay,” Neurocomputing, vol. 73, no. 4, pp. 858–866, 2010. [click]CrossRefGoogle Scholar
  12. [12]
    D. Tong, W. Zhou, X. Zhou, J. Yang, L. Zhang, and Y. Xu. Exponential synchronization for stochastic neural networks with multi-delayed and Markovian switching via adaptive feedback control. Commun. Nonlinear Sci. Numer. Simulat., vol. 29, no. 5, pp. 359–371, 2015.MathSciNetCrossRefGoogle Scholar
  13. [13]
    J. Lu, J. Kurths, J. Cao, N. Mahdavi, and C. Huang, “Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy,” IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 2, pp. 285–292, 2012. [click]CrossRefGoogle Scholar
  14. [14]
    M. Liu, H. Chen, S. Zhang, and W. Sheng, “H synchronization of two different discrete-time chaotic systems via a unified model,” Int. J. Control Autom. Syst., vol. 13, no. 1, pp. 212–221, 2015. [click]CrossRefGoogle Scholar
  15. [15]
    H. Li, “H cluster synchronization and state estimation for complex dynamical networks with mixed time delays,” Appl. Math. Model., vol. 37, no. 12, pp. 7223–7244, 2013. [click]MathSciNetCrossRefGoogle Scholar
  16. [16]
    Q. Gan, R. Hu, and Y. Liang, “Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays,” Commun. Nonlinear Sci. Numer. Simulat., vol. 17, no. 9, pp. 3708–3718, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    D. Tong, Q. Zhu, W. Zhou, Y. Xu, and J. Fang, “Adaptive synchronization for stochastic T-S fuzzy neural networks with time-delay and Markovian jumping parameters,” Neurocomputing, vol. 117, no. 1, pp. 91–97, 2013. [click]CrossRefGoogle Scholar
  18. [18]
    Y. Tang, H. Gao, and J. Kurths, “Distributed robust synchronization of dynamical networks with stochastic coupling,” IEEE Trans. Circuits Syst. Regul. Pap., vol. 61, no. 5, pp. 1508–1519, 2014. [click]MathSciNetCrossRefGoogle Scholar
  19. [19]
    R. Lu, W. Yu, J. Lu, and A. Xue, “Synchronization on complex networks of networks,” IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 11, pp. 2110–2118, 2014. [click]CrossRefGoogle Scholar
  20. [20]
    C. Yuan and X. Mao, “Robust stability and controllability of stochastic differential delay equations with Markovian switching,” Automatica, vol. 40, no. 3, pp. 343–354, 2004. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, World Scientific, 2006.CrossRefzbMATHGoogle Scholar
  22. [22]
    D. Tong, W. Zhou, Y. Gao, C. Ji, and H. Su, “H model reduction for port-controlled Hamiltonian systems,” Appl. Math. Model., vol. 37, no. 5, pp. 2727–2736, 2013. [click]MathSciNetCrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Electronic and Electrical EngineeringShanghai University of Engineering ScienceShanghaiChina
  2. 2.Department of Electronic EngineeringSchool of Information Science and Technology, Fudan UniversityShanghaiChina
  3. 3.College of Information Sciences and TechnologyDonghua UniversityShanghaiChina
  4. 4.School of FinanceNanjing Audit UniversityJiangsuChina

Personalised recommendations