Adaptive synchronization of delayed reaction-diffusion neural networks with unknown non-identical time-varying coupling strengths

This paper concerns the asymptotic synchronization of delayed reaction-diffusion neural networks (RDNNs) with unknown nonidentical time-varying coupling strengths, where the time-varying coupling strengths are consist of continuous time-varying periodic parameters and time-invariant nonnegative parameters. By utilizing a novel adaptive approach, the differential-difference type adaptive laws of coupling strengths and adaptive controller are designed such that the nonidentical RDNNs are asymptotic synchronization. The sufficient conditions dependent on the reaction-diffusion terms are derived by constructing a novel Lyapunov-Krasovskii-like composite energy functional (CEF) and using Barbalat's lemma. Finally, a simulation example is provided to illustrate the effectiveness of the developed approach.

[1]  Junmi Li,et al.  Adaptive Synchronization of Nonlinearly Parameterized Complex Dynamical Networks with Unknown Time-Varying Parameters , 2012 .

[2]  Qian Ma,et al.  Synchronization of stochastic Markovian jump neural networks with reaction-diffusion terms , 2012, Neurocomputing.

[3]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[4]  Rui Yan,et al.  On Repetitive Learning Control for Periodic Tracking Tasks , 2006, IEEE Transactions on Automatic Control.

[5]  Junmin Li,et al.  A new synchronization algorithm for delayed complex dynamical networks via adaptive control approach , 2012 .

[6]  Lei Guo,et al.  Stability analysis of reaction-diffusion Cohen-Grossberg neural networks under impulsive control , 2013, Neurocomputing.

[7]  Sabri Arik,et al.  An analysis of exponential stability of delayed neural networks with time varying delays , 2004, Neural Networks.

[8]  Jianlong Qiu,et al.  Exponential stability of impulsive neural networks with time-varying delays and reaction-diffusion terms , 2007, Neurocomputing.

[9]  Fuad E. Alsaadi,et al.  Receding horizon filtering for a class of discrete time-varying nonlinear systems with multiple missing measurements , 2015, Int. J. Gen. Syst..

[10]  Guo Xiao-Yong,et al.  Projective Synchronization of Complex Dynamical Networks with Time-Varying Coupling Strength via Hybrid Feedback Control , 2011 .

[11]  Jian-Xin Xu,et al.  A new periodic adaptive control approach for time-varying parameters with known periodicity , 2004, IEEE Transactions on Automatic Control.

[12]  Fuad E. Alsaadi,et al.  A new approach to non-fragile state estimation for continuous neural networks with time-delays , 2016, Neurocomputing.

[13]  S. Arik.  Stability analysis of delayed neural networks , 2000 .

[14]  Shuai Liu,et al.  Error-constrained reliable tracking control for discrete time-varying systems subject to quantization effects , 2016, Neurocomputing.

[15]  Junmi Li,et al.  Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays , 2012 .

[16]  Yongkun Li.  Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays , 2004 .

[17]  Junmin Li,et al.  Synchronization of delayed reaction-diffusion neural networks via an adaptive learning control approach , 2013, Comput. Math. Appl..

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

[19]  Jinde Cao,et al.  Synchronization-based approach for parameters identification in delayed chaotic neural networks , 2007 .

[20]  Jing Xu,et al.  Observer based learning control for a class of nonlinear systems with time-varying parametric uncertainties , 2004, IEEE Trans. Autom. Control..

[21]  Junmin Li,et al.  Synchronization for distributed parameter NNs with mixed delays via sampled-data control , 2016, Neurocomputing.

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

[23]  Shengyuan Xu,et al.  Synchronization of stochastic chaotic neural networks with reaction-diffusion terms , 2012 .

[24]  Junmin Li,et al.  Stochastic synchronization for time-varying complex dynamical networks , 2012 .

[25]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

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

[27]  Lei Guo,et al.  Passivity and Stability Analysis of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions , 2011, IEEE Transactions on Neural Networks.

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

[29]  Li Junmin,et al.  Generalized projective synchronization of chaotic systems via adaptive learning control , 2010 .

[30]  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).

[31]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[32]  Junguo Lu,et al.  Global exponential stability and periodicity of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions , 2009 .

[33]  Zidong Wang,et al.  Event-triggered distributed ℋ ∞ state estimation with packet dropouts through sensor networks , 2015 .

[34]  Changyin Sun,et al.  Exponential periodicity and stability of delayed neural networks , 2004, Math. Comput. Simul..

[35]  Zidong Wang,et al.  Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays , 2012, Neurocomputing.

[36]  Junguo Lu.  Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[37]  Fuad E. Alsaadi,et al.  Non-fragile state estimation for discrete Markovian jumping neural networks , 2016, Neurocomputing.

[38]  Qiankun Song,et al.  Novel criteria for global exponential periodicity and stability of recurrent neural networks with time-varying delays , 2008 .

[39]  Qintao Gan,et al.  Global exponential synchronization of generalized stochastic neural networks with mixed time-varying delays and reaction-diffusion terms , 2012, Neurocomputing.

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

[41]  Xuyang Lou,et al.  Asymptotic synchronization of a class of neural networks with reaction-diffusion terms and time-varying delays , 2006, Comput. Math. Appl..

[42]  J. Hale.  Theory of Functional Differential Equations , 1977 .