Asymptotic synchronization for stochastic memristor-based neural networks with noise disturbance

Abstract In this paper, globally asymptotical synchronization for stochastic memristor-based neural networks with random noise disturbance is investigated. Under the framework of differential inclusions theory and set-valued maps, a state feedback controller and an adaptive updated law are designed by constructing a suitable Lyapunov functional. By using Ito formula and some significant inequality techniques, sufficient conditions for the global synchronization of the stochastic memristor-based neural networks which are more general are obtained. Finally, numerical simulations are provided to illustrate the theoretical results.

[1]  Xinsong Yang,et al.  Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication , 2014, Commun. Nonlinear Sci. Numer. Simul..

[2]  Guodong Zhang,et al.  Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control , 2014, Neural Networks.

[3]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[4]  Jianbin Qiu,et al.  Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions , 2013, IEEE Transactions on Fuzzy Systems.

[5]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[6]  Leon O. Chua,et al.  Neural Synaptic Weighting With a Pulse-Based Memristor Circuit , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Hamid Reza Karimi,et al.  New approach to delay-dependent H∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions , 2015, J. Frankl. Inst..

[8]  Shiping Wen,et al.  Synchronization control of stochastic memristor-based neural networks with mixed delays , 2015, Neurocomputing.

[9]  Zhigang Zeng,et al.  Exponential synchronization of memristor-based recurrent neural networks with time delays , 2011, Neurocomputing.

[10]  Lixiang Li,et al.  Synchronization control of memristor-based recurrent neural networks with perturbations , 2014, Neural Networks.

[11]  Meiqin Liu,et al.  Optimal exponential synchronization of general chaotic delayed neural networks: An LMI approach , 2009, Neural Networks.

[12]  Sanbo Ding,et al.  Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays , 2015, Neurocomputing.

[13]  L. Chua.  Memristor-The missing circuit element , 1971 .

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

[15]  Chuandong Li,et al.  Lag quasisynchronization of coupled delayed systems with parameter mismatch by periodically intermittent control , 2013 .

[16]  Guodong Zhang,et al.  Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays , 2013, Neural Networks.

[17]  Jianbin Qiu,et al.  A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Zhigang Zeng,et al.  Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays , 2013, Neural Networks.

[19]  Jianbin Qiu,et al.  Fuzzy-Model-Based Reliable Static Output Feedback $\mathscr{H}_{\infty }$ Control of Nonlinear Hyperbolic PDE Systems , 2016, IEEE Transactions on Fuzzy Systems.

[20]  Leon O. Chua,et al.  Memristor Bridge Synapse-Based Neural Network and Its Learning , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Xinsong Yang,et al.  Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations , 2015, J. Frankl. Inst..

[22]  M. Kisielewicz.  Stochastic differential inclusions and diffusion processes , 2007 .

[23]  Jinde Cao,et al.  New synchronization criteria for memristor-based networks: Adaptive control and feedback control schemes , 2015, Neural Networks.

[24]  Zhigang Zeng,et al.  Synchronization control of a class of memristor-based recurrent neural networks , 2012, Inf. Sci..

[25]  Massimiliano Di Ventra,et al.  Experimental demonstration of associative memory with memristive neural networks , 2009, Neural Networks.

[26]  Richard A. Chapman,et al.  Neural Learning Circuits Utilizing Nano-Crystalline Silicon Transistors and Memristors , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Jun Wang,et al.  Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[28]  Jinde Cao,et al.  Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach , 2014, Neural Networks.

[29]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.