Projective synchronization control of unknown chaotic neural networks with delay and noise perturbation

In this paper, we focus on projective synchronization control of unknown chaotic neural networks, which has time-delay and noise perturbation. Based on Lyapunov method and LMI approach, a controller is designed and some simple criteria are obtained to guarantee the projective synchronization for master and slave unknown chaotic neural networks with time-delay and random noise. Furthermore, a numerical example is given to illustrate the validity of the theoretical results.

[1]  Bishnu Charan Sarkar,et al.  Complete and generalized synchronization of chaos and hyperchaos in a coupled first-order time-delayed system , 2013 .

[2]  Saptarshi Bandyopadhyay,et al.  Phase synchronization control of complex networks of Lagrangian systems on adaptive digraphs , 2013, Autom..

[3]  Wen Liu,et al.  Noisy Chaotic Neural Networks With Variable Thresholds for the Frequency Assignment Problem in Satellite Communications , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[4]  Ping Liu,et al.  Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters , 2011 .

[5]  Evelyn Buckwar,et al.  Exponential stability in p -th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations , 2005 .

[6]  X. Mao,et al.  A note on the LaSalle-type theorems for stochastic differential delay equations , 2002 .

[7]  Lipo Wang,et al.  Applications of transiently chaotic neural networks to image restoration , 2003, International Conference on Neural Networks and Signal Processing, 2003. Proceedings of the 2003.

[8]  M. Rosenblum,et al.  Phase synchronization in driven and coupled chaotic oscillators , 1997 .

[9]  Li Sheng,et al.  Adaptive hybrid lag projective synchronization of unified chaotic systems , 2010, Proceedings of the 29th Chinese Control Conference.

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

[11]  S. Celikovsky,et al.  Efficient chaos shift keying method based on the second error derivative anti-synchronization detection , 2009, 2009 IEEE International Conference on Control and Automation.

[12]  Shihua Zhang,et al.  Adaptive lag synchronization of chaotic Cohen-Grossberg neural networks with discrete delays. , 2012, Chaos.

[13]  L. Arnold Stochastic Differential Equations: Theory and Applications , 1992 .

[14]  Wei Xing Zheng,et al.  Discrete-Time Neural Network for Fast Solving Large Linear $L_{1}$ Estimation Problems and its Application to Image Restoration , 2012, IEEE Transactions on Neural Networks and Learning Systems.

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

[16]  Louis M. Pecora,et al.  Synchronization in Chaotic Systems, Concepts and Applications , 2006 .

[17]  Zhigang Zeng,et al.  Anti-synchronization control of a class of memristive recurrent neural networks , 2013, Commun. Nonlinear Sci. Numer. Simul..

[18]  Baoyun Wang,et al.  To implement the CDMA multiuser detector by using transiently chaotic neural network , 1997 .

[19]  A.N. Pisarchik,et al.  Optical Chaotic Communication Using Generalized and Complete Synchronization , 2010, IEEE Journal of Quantum Electronics.

[20]  Ke Qin,et al.  Projective synchronization of different chaotic neural networks with mixed time delays based on an integral sliding mode controller , 2014, Neurocomputing.

[21]  Xu Yao-qun,et al.  Fourier chaotic neural network with application in optimization , 2008, 2008 27th Chinese Control Conference.

[22]  Jun Yu,et al.  Complete synchronization induced by disorder in coupled chaotic lattices , 2013 .

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

[24]  Jinde Cao,et al.  Anti-synchronization of stochastic perturbed delayed chaotic neural networks , 2009, Neural Computing and Applications.