Projective synchronization of different chaotic neural networks with mixed time delays based on an integral sliding mode controller

In this paper, an integral sliding mode control (SMC) approach is presented to investigate the projective synchronization of nonidentical chaotic neural networks with mixed time delays. By considering a proper sliding surface and constructing Lyapunov-Krasovskii functional, as well as using the linear matrix inequality (LMI) technique, a sliding mode controller is designed to achieve the projective synchronization of the different neural networks. Finally, numerical simulations are carried out to illustrate the effectiveness of the main results.

[1]  Jian Xu,et al.  Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller , 2010, Appl. Math. Comput..

[2]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

[3]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[4]  M. Noorani,et al.  Anti-synchronization of two hyperchaotic systems via nonlinear control , 2009 .

[5]  Yinghai Wang,et al.  Generalized projective synchronization in time-delayed chaotic systems , 2008 .

[6]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[7]  Juan Meng,et al.  GENERALIZED PROJECTIVE SYNCHRONIZATION OF A CLASS OF DELAYED NEURAL NETWORKS , 2008 .

[8]  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.

[9]  B. John Oommen,et al.  Chaotic and pattern recognition properties of a network of Logistic neurons , 2010, 2010 2nd International Conference on Computer Engineering and Technology.

[10]  Yong Chen,et al.  Generalized Q-S (lag, anticipated and complete) synchronization in modified Chua's circuit and Hindmarsh-Rose systems , 2006, Appl. Math. Comput..

[11]  Dibakar Ghosh,et al.  Generalized projective synchronization in time-delayed systems: nonlinear observer approach. , 2009, Chaos.

[12]  V. Singh.  Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

[13]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[14]  K. Aihara,et al.  Chaotic neural networks , 1990 .

[15]  Ju H. Park,et al.  On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays , 2008, Appl. Math. Comput..

[16]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[17]  Jianping Yan,et al.  Generalized projective synchronization of a unified chaotic system , 2005 .

[18]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[19]  J. M. González-Miranda,et al.  Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving , 1998 .

[20]  P. Zhu,et al.  Adaptive synchronization of different Cohen–Grossberg chaotic neural networks with unknown parameters and time-varying delays , 2013, Nonlinear Dynamics.

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

[22]  Guo-Hui Li,et al.  Generalized projective synchronization between two different chaotic systems using active backstepping control , 2006 .

[23]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[24]  Jinde Cao,et al.  Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch , 2011, Nonlinear Dynamics.

[25]  Guohui Li,et al.  Generalized projective synchronization of two chaotic systems by using active control , 2006 .

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

[27]  Yuanwei Jing,et al.  Modified projective synchronization of chaotic systems with disturbances via active sliding mode control , 2010 .

[28]  Lihong Huang,et al.  Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays , 2007 .

[29]  Josef A. Nossek,et al.  A chaotic attractor with cellular neural networks , 1991 .

[30]  Shihua Chen,et al.  Lag synchronizing chaotic system based on a single controller , 2008 .

[31]  Jinde Cao,et al.  Generalized synchronization for delayed chaotic neural networks: a novel coupling scheme , 2006 .