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Periodically Intermittent Synchronization of Stochastic Delayed Neural Networks

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Abstract

In this paper, we focus on the synchronization problem of delayed stochastic neural networks via periodically intermittent control. Two cases of time-varying bounded delay are considered: one is that the time-varying delay without any constraints on the delay derivative, and the other is that the derivative is strictly \({<}1\). For case one, based on piecewise Lyapunov functional-based methods and Razumikhin technique, a mean-square exponential synchronization criterion, which can remove the restriction on the control width and the delay bound, is obtained. For case two, by using a piecewise time-varying Lyapunov functional, convex combination technique, and stochastic analysis technique, a mean-square exponential synchronization criterion that relates to the control period, the control width, and the upper bound on time delay is firstly obtained and formulated in the form of linear matrix inequalities (LMIs). Then, based on the established synchronization criteria, the optimal periodically intermittent synchronization controllers are presented. Finally, three examples are utilized to demonstrate the effectiveness of the new results.

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References

  1. Y. Chen, X. Zhang, G. Shi, H. Tang, Synchronization of delayed chaotic neural networks with stochastic disturbances via periodically intermittent control. 2011 Chinese Control and Decision Conference (CCDC). IEEE (2011), pp. 3882–3887

  2. W.-H. Chen, J. Zhong, Z. Jiang, X. Lu, Periodically intermittent stabilization of delayed neural networks based on piecewise Lyapunov functions/functionals. Circuits Syst. Signal Process. 33(12), 3757–3782 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. W.-H. Chen, W.X. Zheng, On global asymptotic stability of Cohen–Grossberg neural networks with variable delays. IEEE Trans. Circuits Syst. I Regul. Pap. 55(10), 3145–3159 (2008)

    Article  MathSciNet  Google Scholar 

  4. W.-H. Chen, W.X. Zheng, Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays. Automatica 45(6), 1481–1488 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Q. Gan, Global exponential synchronization of generalized stochastic neural networks with mixed time-varying delays and reaction-diffusion terms. Neurocomputing 89, 96–105 (2012)

    Article  Google Scholar 

  6. Q. Gan, Exponential synchronization of stochastic Cohen–Grossberg neural networks with mixed time-varying delays and reaction–diffusion via periodically intermittent control. Neural Netw. 31, 12–21 (2012)

    Article  MATH  Google Scholar 

  7. Q. Gan, Y. Liang, Synchronization of non-identical unknown chaotic delayed neural networks based on adaptive sliding mode control. Neural Process. Lett. 35(3), 245–255 (2012)

    Article  Google Scholar 

  8. C. Hu, J. Yu, H. Jiang, Z. Teng, Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control. Nonlinearity 23, 2369–2390 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. C. Hu, J. Yu, H. Jiang, Finite-time synchronization of delayed neural networks with Cohen–Grossberg type based on delayed feedback control. Neurocomputing 143, 90–96 (2014)

    Article  Google Scholar 

  10. T. Huang, C. Li, X. Liu, Synchronization of chaotic systems with delay using intermittent linear state feedback. Chaos 18, 033122 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Huang, C. Li, Q. Han, Stabilization of delayed chaotic neural networks by periodically intermittent control. Circuits Syst. Signal Process. 28(4), 567–579 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. Jiang, W.-H. Chen, S. Luo, On periodically intermittent stabilization of stochastic delayed neural networks. Control Conference (CCC), 2015 34th Chinese. IEEE (2015), pp. 1781–1786

  13. C. Li, T. Huang, Exponential stability of time-switched two-subsystem nonlinear systems with application to intermittent control. J. Inequal. Appl. 2009, 348242 (2009)

  14. F. Li, P. Shi, L. Wu, X. Zhang, Fuzzy-model-based-stability and nonfragile control for discrete-time descriptor systems with multiple delays. IEEE Trans. Fuzzy Syst. 22(4), 1019–1025 (2014)

    Article  Google Scholar 

  15. F. Li, L. Wu, P. Shi, C.-C. Lim, State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties. Automatica 51, 385–393 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. N. Li, J. Cao, Periodically intermittent control on robust exponential synchronization for switched interval coupled networks. Neurocomputing 131, 52–58 (2014)

    Article  Google Scholar 

  17. X. Li, S. Song, Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method. Commun. Nonlinear Sci. 19(10), 3892–3900 (2014)

    Article  MathSciNet  Google Scholar 

  18. X. Mao, Stochastic Differential Equations and Their Applications (Horwood, Chichester, 1997)

    MATH  Google Scholar 

  19. L. Pan, J. Cao, Stochastic quasi-synchronization for delayed dynamical networks via intermittent control. Commun. Nonlinear Sci. 17(3), 1332–1343 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. J.H. Park, O.M. Kwon, Synchronization of neural networks of neutral type with stochastic perturbation. Mod. Phys. Lett. B 23(14), 1743–1751 (2009)

    Article  MATH  Google Scholar 

  21. H. Shao, G. Miao, Z. Zhang, State feedback control design for a networked control model of systems with two additive time-varying delays. Int. J. Innov. Comput Inf. Control 11(4), 1457–1469 (2015)

    Google Scholar 

  22. Y. Wang, J. Hao, Z. Zuo, A new method for exponential synchronization of chaotic delayed systems via intermittent control. Phys. Lett. A 374, 2024–2029 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Xing, H. Jiang, C. Hu, Exponential synchronization for delayed recurrent neural networks via periodically intermittent control. Neurocomputing 113, 122–129 (2013)

    Article  Google Scholar 

  24. C. Xu, M. Liao, Q. Zhang, On the mean square exponential stability for a stochastic fuzzy cellular neural network with distributed delays and time-varying delays. Int. J. Innov. Comput. Inf. Control 11(1), 247–255 (2015)

    Google Scholar 

  25. X. Yang, J. Cao, Stochastic synchronization of coupled neural networks with intermittent control. Phys. Lett. A 373(36), 3259–3272 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. T. Yang, L.O. Chua, Generalized synchronization of chaos via linear transformations. Int. J. Bifurc. Chaos 9(01), 215–219 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  27. G. Zhang, X. Lin, X. Zhang, Exponential stabilization of neutral-type neural networks with mixed interval time-varying delays by intermittent control: a CCL approach. Circuits Syst. Signal Process. 33(2), 371–391 (2014)

    Article  Google Scholar 

  28. W. Zhang, C. Li, T. Huang, J. Qi, Global stability and synchronization of Markovian switching neural networks with stochastic perturbation and impulsive delay. Circuits Syst. Signal Process. 34(8), 2457–2474 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  29. W. Zhou, Q. Zhu, P. Shi, H. Su, J. Fang, L. Zhou, Adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching parameters. IEEE Trans. Cybern. 44(12), 2848–2860 (2014)

    Article  Google Scholar 

  30. Q. Zhu, W. Zhou, D. Tong, J. Fang, Adaptive synchronization for stochastic neural networks of neutral-type with mixed time-delays. Neurocomputing 99, 477–485 (2013)

    Article  Google Scholar 

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Acknowledgments

The authors would like to thank the editor and the anonymous reviewers for their valuable comments and constructive suggestions. This work was supported by the Innovation Project of Guangxi Graduate Education (YCSZ2014036 and YCSZ2015031).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, Guangxi, People’s Republic of China

    Yan Jiang & Shixian Luo

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  1. Yan Jiang
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  2. Shixian Luo
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Correspondence to Shixian Luo.

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Jiang, Y., Luo, S. Periodically Intermittent Synchronization of Stochastic Delayed Neural Networks. Circuits Syst Signal Process 36, 1426–1444 (2017). https://doi.org/10.1007/s00034-016-0377-5

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