Synchronisation of chaotic neural networks with unknown parameters and random time-varying delays based on adaptive sampled-data control and parameter identification

This study investigates the synchronisation problem of chaotic neural networks with unknown parameters and random time-varying delays. By introducing a stochastic variable with Bernoulli distribution, the neural networks with random time-varying delays is transformed into one with deterministic varying delays and stochastic parameters. A simple and robust adaptive sampled-data controller is designed such that the response system can be synchronised with a drive system with unknown parameters by using suitable parameter identification and the Lyapunov stability theory. The proposed synchronisation criteria are easily verified and do not need to solve any linear matrix inequality. Numerical simulations are carried out to demonstrate the effectiveness of the established synchronisation laws.

[1]  Hamid Khaloozadeh,et al.  Stable chaos synchronisation scheme for non-linear uncertain systems , 2010 .

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

[3]  Hak-Keung Lam,et al.  Chaotic synchronisation using output/full state-feedback polynomial controller , 2010 .

[4]  Pagavathigounder Balasubramaniam,et al.  Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays , 2010, Fuzzy Sets Syst..

[5]  Nejat Olgac,et al.  Application of sliding mode control to swarms under conflict , 2011 .

[6]  Jian Xu,et al.  Synchronization and synchronized periodic solution in a simplified five-neuron BAM neural network with delays , 2011, Neurocomputing.

[7]  Haiyan Hu,et al.  Hopf bifurcation analysis of a four-neuron network with multiple time delays , 2009 .

[8]  Hak-Keung Lam,et al.  Chaotic Synchronization Using Sampled-Data Fuzzy Controller Based on Fuzzy-Model-Based Approach , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Rui Xu,et al.  Synchronization of chaotic neural networks with mixed time delays , 2011 .

[10]  Maoan Han,et al.  Exponential lag synchronization of delayed fuzzy cellular neural networks with impulses , 2009 .

[11]  Xiaoming Xu,et al.  Synchronisation analysis and impulsive control of complex networks with coupling delays , 2009 .

[12]  V. Kapila,et al.  Master–slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators , 2010 .

[13]  Ju H. Park.  A novel criterion for global asymptotic stability of BAM neural networks with time delays , 2006 .

[14]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[15]  Jinde Cao,et al.  Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters , 2008 .

[16]  Li Sheng,et al.  Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms , 2009 .

[17]  Tiedong Ma,et al.  Delay-probability-distribution-dependent robust stability analysis for stochastic neural networks with time-varying delay , 2009 .

[18]  Dong Yue,et al.  Delay-Distribution-Dependent Exponential Stability Criteria for Discrete-Time Recurrent Neural Networks With Stochastic Delay , 2008, IEEE Transactions on Neural Networks.

[19]  Zhidong Teng,et al.  Exponential synchronization of Cohen-Grossberg neural networks via periodically intermittent control , 2011, Neurocomputing.

[20]  R. Rakkiyappan,et al.  Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays , 2011 .

[21]  Jun-an Lu,et al.  Using sampled-data feedback control and linear feedback synchronization in a new hyperchaotic system , 2008 .

[22]  Zuo-Lei Wang,et al.  Anti-synchronization of Liu system and Lorenz system with known or unknown parameters , 2009 .

[23]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[24]  Zidong Wang,et al.  Improved sliding mode control for discrete-time systems via reaching law , 2010 .

[25]  X. Liao,et al.  Stability analysis of genetic regulatory network with time delays and parameter uncertainties , 2010 .

[26]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[27]  Jinde Cao,et al.  Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay , 2011, Neural Networks.

[28]  Huaguang Zhang,et al.  Improved Robust Stability Criteria for Delayed Cellular Neural Networks via the LMI Approach , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Alireza Mohammad Shahri,et al.  Adaptive robust time-varying control of uncertain non-holonomic robotic systems , 2012 .

[30]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[31]  Yong He,et al.  Exponential synchronization of neural networks with time-varying mixed delays and sampled-data , 2010, Neurocomputing.

[32]  James Lam,et al.  New Stability Criteria for Neural Networks with Distributed and Probabilistic Delays , 2009, Circuits Syst. Signal Process..

[33]  Dong Yue,et al.  Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay , 2009, Neurocomputing.

[34]  Zijiang Yang,et al.  Lag Synchronization of Unknown Chaotic Delayed Yang–Yang-Type Fuzzy Neural Networks With Noise Perturbation Based on Adaptive Control and Parameter Identification , 2009, IEEE Transactions on Neural Networks.

[35]  Min Wu,et al.  Improved Global Asymptotical Synchronization of Chaotic Lur'e Systems With Sampled-Data Control , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[36]  V. Singh,et al.  Improved global robust stability criterion for interval delayed neural networks - brief paper , 2009 .

[37]  Jun-Guo Lu,et al.  Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach , 2009 .

[38]  Jinde Cao,et al.  Synchronization of a class of delayed neural networks with reaction–diffusion terms☆ , 2007 .

[39]  Jinde Cao,et al.  Cluster synchronization in an array of coupled stochastic delayed neural networks via pinning control , 2011, Neurocomputing.

[40]  Runhe Qiu,et al.  Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays☆ , 2008 .