Synchronization of Non-Identical Unknown Chaotic Delayed Neural Networks Based on Adaptive Sliding Mode Control

The synchronization problem is studied in this paper for non-identical chaotic neural networks with time delays and fully unknown parameters, where the mismatched parameters, activation functions and neural network architectures are taken into account. To overcome the difficulty that complete synchronization of non-identical chaotic neural networks cannot be achieved only by utilizing output feedback control, we design an adaptive sliding mode controller to realize the synchronization. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. These results generalize a few previous known results and remove some restrictions on the parameters, activation functions and neural network architectures. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.

[1]  Ju H. Park,et al.  Synchronization Criterion for Lur’e Systems via Delayed PD Controller , 2010, J. Optim. Theory Appl..

[2]  Chun-Lai Li,et al.  Tracking control and generalized projective synchronization of a class of hyperchaotic system with unknown parameter and disturbance , 2012 .

[3]  Ju H. Park,et al.  Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay , 2010 .

[4]  Wei Ding,et al.  Synchronization for delayed non-autonomous reaction–diffusion fuzzy cellular neural networks , 2012 .

[5]  Li Yang,et al.  Anti-periodic solutions for a class of Cohen–Grossberg neural networks with time-varying delays on time scales , 2011, Int. J. Syst. Sci..

[6]  Yugang Niu,et al.  Sliding mode control for a class of nonlinear discrete-time networked systems with multiple stochastic communication delays , 2011, Int. J. Syst. Sci..

[7]  D. H. Ji,et al.  Synchronization of neutral complex dynamical networks with coupling time-varying delays , 2011 .

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

[9]  Sabri Arik,et al.  New results for robust stability of dynamical neural networks with discrete time delays , 2010, Expert Syst. Appl..

[10]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

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

[12]  Zidong Wang,et al.  Robust synchronisation of delayed neural networks with both linear and non-linear couplings , 2009, Int. J. Syst. Sci..

[13]  Xiaoshan Zhao,et al.  Generalized function projective synchronization of two different hyperchaotic systems with unknown parameters , 2011 .

[14]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[15]  Ju H. Park,et al.  A new stability criterion for bidirectional associative memory neural networks of neutral-type , 2008, Appl. Math. Comput..

[16]  M. Yahyazadeh,et al.  Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control. , 2011, ISA transactions.

[17]  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.

[18]  Gang Feng,et al.  Synchronization of nonidentical chaotic neural networks with time delays , 2009, Neural Networks.

[19]  Xiaowu Mu,et al.  Synchronization of the near-identical chaotic systems with the unknown parameters , 2010 .

[20]  Ju H. Park.  Synchronization of cellular neural networks of neutral type via dynamic feedback controller , 2009 .

[21]  Sohrab Khanmohammadi,et al.  Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller , 2011 .

[22]  Daoyi Xu,et al.  Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays , 2011, Neurocomputing.

[23]  Yang Tang,et al.  Controller design for synchronization of an array of delayed neural networks using a controllable probabilistic PSO , 2011, Inf. Sci..

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

[25]  Zidong Wang,et al.  On synchronization of coupled neural networks with discrete and unbounded distributed delays , 2008, Int. J. Comput. Math..

[26]  Mohammad Ataei,et al.  A chattering-free sliding mode control design for uncertain chaotic systems , 2009 .

[27]  Ju H. Park,et al.  LMI optimization approach on stability for delayed neural networks of neutral-type , 2008, Appl. Math. Comput..

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