Robust Adaptive Synchronization Control for a Class of Perturbed and Delayed Neural Networks

This paper is concerned with the asymptotic synchronization problem of a general neural network using the robust adaptive control technique. It is considered a class of modified Cohen–Grossberg neural networks which is supposed to undergo unknown perturbations caused by state-independent nonlinearities and bounded mixed time-varying delays on neuron amplification and activation functions. An adaptive compensation control strategy is proposed to ensure the elimination of the perturbed and delayed effects by means of adaptive estimations of unknown controller parameters. Through Lyapunov stability theory, it is shown that the proposed adaptive compensation controllers can guarantee the asymptotic synchronization of neural networks without knowing the knowledge of bounds of nonlinearities and delays. A numerical example is provided to illustrate the effectiveness of the developed techniques.

[1]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[2]  Hongbin Zhang,et al.  Global exponential stability of impulsive fuzzy Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms , 2012, Neurocomputing.

[3]  Jinde Cao,et al.  Synchronization control of stochastic delayed neural networks , 2007 .

[4]  Jun Zhao,et al.  Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes , 2009 .

[5]  Huijun Gao,et al.  Novel Robust Stability Criteria for Stochastic Hopfield Neural Networks With Time Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Guo-Ping Liu,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay , 2007, IEEE Transactions on Neural Networks.

[7]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  Tianping Chen,et al.  Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix , 2008 .

[9]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[10]  Lei Guo,et al.  Adaptive Statistic Tracking Control Based on Two-Step Neural Networks With Time Delays , 2009, IEEE Transactions on Neural Networks.

[11]  José J. Oliveira.  Global stability of a Cohen–Grossberg neural network with both time-varying and continuous distributed delays , 2011 .

[12]  Jinde Cao,et al.  Robust Stability of Switched Cohen–Grossberg Neural Networks With Mixed Time-Varying Delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Xinchun Jia,et al.  Dynamical analysis of Cohen-Grossberg neural networks with finite and infinite delays , 2009, Appl. Math. Comput..

[14]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[15]  Jun Wang,et al.  Robustness Analysis of Global Exponential Stability of Recurrent Neural Networks in the Presence of Time Delays and Random Disturbances , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Shengyuan Xu,et al.  Novel global asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  Zidong Wang,et al.  Bounded $H_{\infty}$ Synchronization and State Estimation for Discrete Time-Varying Stochastic Complex Networks Over a Finite Horizon , 2011, IEEE Transactions on Neural Networks.

[18]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[19]  Hongxing Yao,et al.  Adaptive synchronization of bipartite dynamical networks with distributed delays and nonlinear derivative coupling , 2011 .

[20]  Jinde Cao,et al.  Robust Adaptive Control of Unknown Modified Cohen–Grossberg Neural Networks With Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[21]  Wei Xing Zheng,et al.  Stability and $L_{2}$ Performance Analysis of Stochastic Delayed Neural Networks , 2011, IEEE Transactions on Neural Networks.

[22]  Chien-Yu Lu,et al.  Design of Delay-Dependent Exponential Estimator for T–S Fuzzy Neural Networks with Mixed Time-Varying Interval Delays Using Hybrid Taguchi-Genetic Algorithm , 2012, Neural Processing Letters.

[23]  Tianping Chen,et al.  Nonnegative periodic dynamics of delayed Cohen-Grossberg neural networks with discontinuous activations , 2010, Neurocomputing.

[24]  Mario di Bernardo,et al.  Novel decentralized adaptive strategies for the synchronization of complex networks , 2009, Autom..

[25]  Petros A. Ioannou,et al.  Robust Adaptive Control , 2012 .

[26]  Zhanshan Wang,et al.  Improved Stability Results for Stochastic Cohen–Grossberg Neural Networks with Discrete and Distributed Delays , 2011, Neural Processing Letters.

[27]  Guanrong Chen,et al.  Robust adaptive synchronization of uncertain dynamical networks , 2004 .

[28]  Huan Su,et al.  Global stability for discrete Cohen-Grossberg neural networks with finite and infinite delays , 2012, Appl. Math. Lett..

[29]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[30]  Guang-Hong Yang,et al.  Adaptive Pinning Control of Deteriorated Nonlinear Coupling Networks With Circuit Realization , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Tianping Chen,et al.  Robust synchronization of delayed neural networks based on adaptive control and parameters identification , 2006 .

[32]  Jinde Cao,et al.  Impulsive Effects on Stability of Fuzzy Cohen–Grossberg Neural Networks With Time-Varying Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

[34]  Lihong Huang,et al.  Stability analysis of Cohen–Grossberg neural networks with discontinuous neuron activations , 2010 .

[35]  Qiankun Song,et al.  Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling , 2010, Appl. Math. Comput..

[37]  Huaguang Zhang,et al.  Global Asymptotic Stability and Robust Stability of a Class of Cohen-Grossberg Neural Networks With Mixed Delays , 2009, IEEE Trans. Circuits Syst. I Regul. Pap..

[38]  Zidong Wang,et al.  State Estimation for Discrete-Time Neural Networks with Markov-Mode-Dependent Lower and Upper Bounds on the Distributed Delays , 2012, Neural Processing Letters.

[39]  Vimal Singh,et al.  Global robust stability of delayed neural networks: an LMI approach , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[40]  J. Hopfield.  Neurons withgraded response havecollective computational properties likethoseoftwo-state neurons , 1984 .

[41]  Stephen P. Boyd,et al.  Analysis and Synthesis of State-Feedback Controllers With Timing Jitter , 2009, IEEE Transactions on Automatic Control.

[42]  Shengyuan Xu,et al.  Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.