Impulsive Synchronization of Stochastic Neural Networks via Controlling Partial States

In the paper, synchronization problem for stochastic neural networks are studied by impulsively controlling partial states. At each impulsive instant, only part of the states are controlled to realize the synchronization of impulsively coupled stochastic neural networks. By using the method of average impulsive interval, less conservative synchronization criteria are derived. The derived sufficient conditions are closely related to the parameters of system dynamics, impulsive gain, impulsive interval and the proportion of the controlled components. Finally, numerical example is given to illustrate the effectiveness of our theoretical results.

[1]  Yonghui Xia,et al.  Almost Automorphic Solutions of Impulsive Cellular Neural Networks with Piecewise Constant Argument , 2014, Neural Processing Letters.

[2]  J. Kurths,et al.  Detecting phase synchronization by localized maps: Application to neural networks , 2007, 0706.3317.

[3]  L. Chua,et al.  A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS , 1994 .

[4]  Ximei Liu,et al.  New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems , 2014, Nonlinear Dynamics.

[5]  Tomasz Kapitaniak,et al.  Synchronized pendula: From Huygens’ clocks to chimera states , 2014 .

[6]  Jinde Cao,et al.  Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach , 2015, Neural Networks.

[7]  Qiang Xi,et al.  Global Exponential Stability of Cohen-Grossberg Neural Networks with Piecewise Constant Argument of Generalized Type and Impulses , 2016, Neural Computation.

[8]  Jinde Cao,et al.  Exponential H∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities , 2016, Science China Technological Sciences.

[9]  Zhengguo Li,et al.  Analysis and design of impulsive control systems , 2001, IEEE Trans. Autom. Control..

[10]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[11]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Andreas Amann,et al.  Analytical limitation for time-delayed feedback control in autonomous systems. , 2011, Physical review letters.

[13]  Wenbing Zhang,et al.  Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. , 2013, IEEE transactions on neural networks and learning systems.

[14]  Jinde Cao,et al.  Exponential stability of high-order bidirectional associative memory neural networks with time delays , 2004 .

[15]  Jinde Cao,et al.  Synchronization of delayed complex dynamical networks with impulsive and stochastic effects , 2011 .

[16]  Zhidong Teng,et al.  Globally Exponential Stability for Delayed Neural Networks Under Impulsive Control , 2010, Neural Processing Letters.

[17]  Yang Liu,et al.  Controllability of Boolean control networks with impulsive effects and forbidden states , 2014 .

[18]  Gang Feng,et al.  Synchronization of Complex Dynamical Networks With Time-Varying Delays Via Impulsive Distributed Control , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Zhigang Zeng,et al.  Exponential Adaptive Lag Synchronization of Memristive Neural Networks via Fuzzy Method and Applications in Pseudorandom Number Generators , 2014, IEEE Transactions on Fuzzy Systems.

[20]  Yang Liu,et al.  A New Fuzzy Impulsive Control of Chaotic Systems Based on T–S Fuzzy Model , 2011, IEEE Transactions on Fuzzy Systems.

[21]  Bin Liu,et al.  Stability of Solutions for Stochastic Impulsive Systems via Comparison Approach , 2008, IEEE Transactions on Automatic Control.

[22]  Jinde Cao,et al.  Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers , 2015, J. Frankl. Inst..

[23]  Frank C. Hoppensteadt,et al.  Pattern recognition via synchronization in phase-locked loop neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[24]  Jinde Cao,et al.  Pinning impulsive stabilization of nonlinear Dynamical Networks with Time-Varying Delay , 2012, Int. J. Bifurc. Chaos.

[25]  Zabih Ghassemlooy,et al.  Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback. , 2016, Chaos.

[26]  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..

[27]  F. Zou,et al.  Bifurcation and chaos in cellular neural networks , 1993 .

[28]  Jianquan Lu,et al.  Stability and L 2-gain performance for non-linear switched impulsive systems , 2015 .

[29]  J. Suykens,et al.  Impulsive Synchronization of Chaotic Lur'e Systems by Measurement Feedback , 1998 .

[30]  Jinde Cao,et al.  Synchronization of Randomly Coupled Neural Networks With Markovian Jumping and Time-Delay , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[31]  Ruggero Carli,et al.  Network Clock Synchronization Based on the Second-Order Linear Consensus Algorithm , 2014, IEEE Transactions on Automatic Control.

[32]  Tao Yang,et al.  Impulsive Systems and Control: Theory and Applications , 2001 .

[33]  Sundarapandian Vaidyanathan Global Chaos Synchronization of Hyperchaotic Pang and Hyperchaotic Wang Systems via Adaptive Control , 2011 .

[34]  Jinde Cao,et al.  Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  Zhengwen Tu,et al.  Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays , 2017, Neural Processing Letters.

[36]  Yang Tang,et al.  Exponential Synchronization of Coupled Switched Neural Networks With Mode-Dependent Impulsive Effects , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Yang Liu,et al.  New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays , 2012, Math. Comput. Model..

[38]  Long Zhou,et al.  Chaos Multiscale-Synchronization between Two Different fractional-Order hyperchaotic Systems Based on Feedback Control , 2013, Int. J. Bifurc. Chaos.

[39]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[40]  Sundarapandian Vaidyanathan,et al.  Chaos Modeling and Control Systems Design , 2014, Chaos Modeling and Control Systems Design.

[41]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[42]  Bo Wu,et al.  A Halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays , 2015, Appl. Math. Comput..