Periodically Intermittent Synchronization of Stochastic Delayed Neural Networks

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 $${<}1$$<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.

[1]  Qintao Gan,et al.  Synchronization of Non-Identical Unknown Chaotic Delayed Neural Networks Based on Adaptive Sliding Mode Control , 2012, Neural Processing Letters.

[2]  Shiji Song,et al.  Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method , 2014, Commun. Nonlinear Sci. Numer. Simul..

[3]  Ligang Wu,et al.  State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties , 2015, Autom..

[4]  Xian Zhang,et al.  Fuzzy-Model-Based ${{\cal D}}$-Stability and Nonfragile Control for Discrete-Time Descriptor Systems With Multiple Delays , 2014, IEEE Transactions on Fuzzy Systems.

[5]  Jinde Cao,et al.  Stochastic synchronization of coupled neural networks with intermittent control , 2009 .

[6]  Qingyu Zhu,et al.  Adaptive synchronization for stochastic neural networks of neutral-type with mixed time-delays , 2013, Neurocomputing.

[7]  L. Chua,et al.  Generalized synchronization of chaos via linear transformations , 1999 .

[8]  Qintao Gan,et al.  Global exponential synchronization of generalized stochastic neural networks with mixed time-varying delays and reaction-diffusion terms , 2012, Neurocomputing.

[9]  Jinde Cao,et al.  Stochastic quasi-synchronization for delayed dynamical networks via intermittent control , 2012 .

[10]  Zhidong Teng,et al.  Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control , 2010 .

[11]  Wei Xing Zheng,et al.  On Global Asymptotic Stability of Cohen–Grossberg Neural Networks With Variable Delays , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[12]  Haijun Jiang,et al.  Exponential synchronization for delayed recurrent neural networks via periodically intermittent control , 2013, Neurocomputing.

[13]  Guiyin Shi,et al.  Synchronization of delayed chaotic neural networks with stochastic disturbances via periodically intermittent control , 2011, 2011 Chinese Control and Decision Conference (CCDC).

[14]  Chuandong Li,et al.  Synchronization of chaotic systems with delay using intermittent linear state feedback. , 2008, Chaos.

[15]  Wei Xing Zheng,et al.  Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays , 2009, Autom..

[16]  Jinde Cao,et al.  Periodically intermittent control on robust exponential synchronization for switched interval coupled networks , 2014, Neurocomputing.

[17]  Chuandong Li,et al.  Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control , 2009 .

[18]  Chuandong Li,et al.  Stabilization of Delayed Chaotic Neural Networks by Periodically Intermittent Control , 2009, Circuits Syst. Signal Process..

[19]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[20]  Peng Shi,et al.  Adaptive Synchronization for Neutral-Type Neural Networks with Stochastic Perturbation and Markovian Switching Parameters , 2014, IEEE Transactions on Cybernetics.

[21]  Z. Zuo,et al.  A new method for exponential synchronization of chaotic delayed systems via intermittent control , 2010 .

[22]  Ju H. Park,et al.  SYNCHRONIZATION OF NEURAL NETWORKS OF NEUTRAL TYPE WITH STOCHASTIC PERTURBATION , 2009 .

[23]  Wu‐Hua Chen,et al.  On periodically intermittent stabilization of stochastic delayed neural networks , 2015, 2015 34th Chinese Control Conference (CCC).

[24]  Wei Zhang,et al.  Global Stability and Synchronization of Markovian Switching Neural Networks with Stochastic Perturbation and Impulsive Delay , 2015, Circuits Syst. Signal Process..

[25]  Xian Zhang,et al.  Exponential Stabilization of Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays by Intermittent Control: A CCL Approach , 2014, Circuits Syst. Signal Process..

[26]  Qintao Gan,et al.  Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control , 2012, Neural Networks.

[27]  Haijun Jiang,et al.  Finite-time synchronization of delayed neural networks with Cohen-Grossberg type based on delayed feedback control , 2014, Neurocomputing.

[28]  Wu-Hua Chen,et al.  Periodically Intermittent Stabilization of Delayed Neural Networks Based on Piecewise Lyapunov Functions/Functionals , 2014, Circuits Syst. Signal Process..