Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach

Abstract In this paper, impulsive control for master–slave synchronization schemes consisting of identical chaotic neural networks is studied. Impulsive control laws are derived based on linear static output feedback. A sufficient condition for global asymptotic synchronization of master–slave chaotic neural networks via output feedback impulsive control is established, in which synchronization is proven in terms of the synchronization errors between the full state vectors. An LMI-based approach for designing linear static output feedback impulsive control laws to globally asymptotically synchronize chaotic neural networks is discussed. With the help of LMI solvers, linear output feedback impulsive controllers can be easily obtained along with the bounds of the impulsive intervals for global asymptotic synchronization. The method is finally illustrated by numerical simulations.

[1]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[2]  R. Desimone,et al.  Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention , 2001, Science.

[3]  Qidi Wu,et al.  Impulsive control for the stabilization and synchronization of Lorenz systems , 2002 .

[4]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[5]  Tingwen Huang,et al.  Impulsive stabilization and synchronization of a class of chaotic delay systems. , 2005, Chaos.

[6]  Jinde Cao,et al.  Stability and Hopf Bifurcation in a Simplified BAM Neural Network With Two Time Delays , 2007, IEEE Transactions on Neural Networks.

[7]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[8]  L. Chua,et al.  Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication , 1997 .

[9]  A. Das,et al.  Chaos in a Three-Dimensional General Model of Neural Network , 2002, Int. J. Bifurc. Chaos.

[10]  Zhigang Zeng,et al.  Improved conditions for global exponential stability of recurrent neural networks with time-varying delays , 2006, IEEE Transactions on Neural Networks.

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

[12]  David J. Hill,et al.  A Hybrid impulsive and Switching Control Strategy for Synchronization of Nonlinear Systems and Application to Chua's Chaotic Circuit , 2006, Int. J. Bifurc. Chaos.

[13]  Parlitz,et al.  Driving and synchronizing by chaotic impulses. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Xiaofeng Liao,et al.  Complete and lag synchronization of hyperchaotic systems using small impulses , 2004 .

[15]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[16]  Carlos Lourenço,et al.  Brain Chaos and Computation , 1996, Int. J. Neural Syst..

[17]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[18]  Jinde Cao,et al.  Robust impulsive synchronization of coupled delayed neural networks with uncertainties , 2007 .

[19]  Y. Soh,et al.  The stabilization and synchronization of Chua's oscillators via impulsive control , 2001 .

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

[21]  Yeng Chai Soh,et al.  Synchronization of Lorenz Systems via impulsive Control and Sporadic Coupling , 2004, Int. J. Bifurc. Chaos.

[22]  Tianping Chen,et al.  Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling , 2007 .

[23]  Chun-Mei Yang,et al.  Impulsive synchronization of Lorenz systems , 1997 .

[24]  Changyun Wen,et al.  Impulsive control for the stabilization and synchronization of Lorenz systems , 2000 .

[25]  Leon O. Chua,et al.  Cellular Neural Networks and Visual Computing: Foundations and Applications , 2002 .

[26]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[27]  Leon O. Chua,et al.  Conditions for impulsive Synchronization of Chaotic and hyperchaotic Systems , 2001, Int. J. Bifurc. Chaos.

[28]  Guanrong Chen,et al.  Chaos quasisynchronization induced by impulses with parameter mismatches. , 2006, Chaos.

[29]  Leon O. Chua,et al.  Impulsive synchronization of chaotic Lur'e systems: state feedback case , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[30]  Xinzhi Liu,et al.  Robust impulsive synchronization of uncertain dynamical networks , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

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

[33]  E. Niebur,et al.  Growth patterns in the developing brain detected by using continuum mechanical tensor maps , 2022 .

[34]  Xinzhi Liu,et al.  Application of Impulsive Synchronization to Communication Security , 2003 .

[35]  Yan Huang,et al.  A New Class of Chaotic Simple Three-Neuron Cellular Neural Networks , 2006, Int. J. Bifurc. Chaos.

[36]  Chi-Chuan Hwang,et al.  Exponential synchronization of a class of neural networks with time-varying delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).