Fixed-time control synchronization of stochastic memristive neural networks with time-varying delays

Abstract

Abstract: The fixed-time control synchronization of stochastic memristive neural networks with time-varying delays is studied. Based on the set-valued mapping, stochastic differential inclusion theory, fixed-time stability theory, Lyapunov function, I$\hat{t}$o's formula and some inequality methods, under the appropriate feedback control u_i(t) which related to delay τ, statistics perturbation term and transition jump T_i, some new sufficient condition is obtained for fixed time control synchronization.

Key words: Memristive neural network, fixed-time synchronization, switching jumps, stochastic perturbations, time-varying delays, p-norm

CLC Number:

O175.1

PU Hao, HUANG Jiang-wen, QIN Jin, WANG Zheng-wei, WANG Xing. Fixed-time control synchronization of stochastic memristive neural networks with time-varying delays[J]. Journal of Lanzhou University of Technology, 2020, 46(5): 158-165.

References

[1] CHUA L O.Memristor-the missing circuit element[J].IEEE Transactions on Circuit Theory,1971,18(5):507-519.
[2] STRUKOV D B,SNIDER G S,STEWART D R,et al.The missing memristor found[J].Nature,2008,453:80-83.
[3] HU X F,DUAN S K,WANG L D.Memristive multilevel memory with applications in audio signal storage[J].Lecture Notes in Computer Science,2011,1:228-235.
[4] WANG S F.Dynamical analysis of memristive unified chaotic system and its application in secure communication[J].IEEE Access,2018,6:66055-66061.
[5] ZHA J X,HUANG H,HUANG T W,et al.A general memristor model and its applications in programmable analog circuits[J].Neurocomputing,2017,267(6):134-140.
[6] WANG B,ZOU F C,CHENG J.Original research article a memristor-based chaotic system and its application in image encryption[J].Optik-International Journal for Light and Electron Optics,2018,154:538-544.
[7] SHI X L,DUAN S K,WANG L D,et al.A novel memristive electronic synapse-based Hermite chaotic neural network with application in cryptography[J].Neurocomputing,2015,166:487-495.
[8] ZHANG G D,SHEN Y I.Exponential synchronization of Delayed memristor-based chaotic neural networks via periodically intermittent control[J].Neural Networks,2014,55:1-10.
[9] ABDURAHMAN A,JIANG H J,HU C.General decay synchronization of memristor-based Cohen-Grossberg neural networks with mixed time-delays and discontinuous activations[J].Journal of the Franklin Institute,2017,354:7028-7052.
[10] LI N,CAO J D.New synchronization criteria for memristor-based networks:Adaptive control and feedback control schemes[J].Neural Networks,2015,61:1-9.
[11] WANG X,SHE K,ZHONG S M,et al.Exponential synchronization of memristor-based neural networks with time-varying delay and stochastic perturbation[J].Neurocomputing,2017,242:131-139.
[12] CHEN C,CHUAN C,LI L X,et al.Finite-time synchronization of memristor-based neural networks with mixed delays[J].Neurocomputing,2017,235:83-89.
[13] ABDURAHMAN A,JIANG H J,TENG Z D.Finite-time synchronization for memristor-based neural networks with time-varying delays[J].Neural Networks,2015,69:20-28.
[14] RYAN E E.Finite-time stabilization of uncertain nonlinear planar systems[J].Dynamics and Control,1991,1:83-94.
[15] POLYAKOV A.Nonlinear feedback design for fixed-time stabilization of linear control systems[J].IEEE Transactions on Automatic Control,2012,57(8):2106-2110.
[16] CHEN C,LI L X,PENG H P,et al.Fixed-time synchronization of inertial memristor-based neural networks with discrete delay[J].Neural Networks,2019,109:81-89.
[17] ZHEN M W,LI L X,XIAO J H,et al.Fixed-time synchronization of memristor-based fuzzy cellular neural network with time-varying delay[J].Journal of the Franklin Institute,2018,355:6780-6809.
[18] WEI R Y,CAO J D,ALSAED A.Finite-time and fixed-time synchro nization analysis of inertial memristive neural networks with time-varying delays[J].Cogn Neurodyn,2018,12:121-134.
[19] LU H,HE W L,HAN Q L,et al.Fixed-time synchronization for coupled delayed neural networks with discontinuous or continuous activations[J].Neurocomputing,2018,314:143-153.
[20] DING S B,WANG Z S.Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays[J].Neurocomputing,2015,162:16-25.
[21] ZHANG B,DENG F Q,XIE S L,et al.Exponential synchronization of stochastic time-delayed memristor-based neural networks via distributed impulsive control[J].Neurocomputing,2018,286:41-50.
[22] HAN X M,WU H Q,FANG B L.Adaptive exponential synchronization of memristive neural networks with mixed time-varying delays[J].Neurocomputing,2016,201:40-50.