Finite-time synchronization of memristor neural networks via interval matrix method

In this paper, the finite-time synchronization problems of two types of driven-response memristor neural networks (MNNs) without time-delay and with time-varying delays are investigated via interval matrix method, respectively. Based on interval matrix transformation, the driven-response MNNs are transformed into a kind of system with interval parameters, which is different from the previous research approaches. Several sufficient conditions in terms of linear matrix inequalities (LMIs) are driven to guarantee finite-time synchronization for MNNs. Correspondingly, two types of nonlinear feedback controllers are designed. Meanwhile, the upper-bounded of the settling time functions are estimated. Finally, two numerical examples with simulations are given to illustrate the correctness of the theoretical results and the effectiveness of the proposed controllers.

[1]  Quan Yin,et al.  Passivity analysis for memristor-based recurrent neural networks with discrete and distributed delays , 2015, Neural Networks.

[2]  Zhigang Zeng,et al.  Scale-Limited Lagrange Stability and Finite-Time Synchronization for Memristive Recurrent Neural Networks on Time Scales , 2017, IEEE Transactions on Cybernetics.

[3]  Zhigang Zeng,et al.  A memristor-based neural network circuit with synchronous weight adjustment , 2019, Neurocomputing.

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

[5]  Olga I. Moskalenko,et al.  On the use of chaotic synchronization for secure communication , 2009 .

[6]  Jing Zhang,et al.  Command Filter-Based Adaptive Fuzzy Control for Nonlinear Systems With Unknown Control Directions , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[7]  Zhigang Zeng,et al.  Synchronization of Switched Neural Networks With Communication Delays via the Event-Triggered Control , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Fuad E. Alsaadi,et al.  A new switching control for finite-time synchronization of memristor-based recurrent neural networks , 2017, Neural Networks.

[9]  Zhigang Zeng,et al.  Synchronization of Multiple Reaction–Diffusion Neural Networks With Heterogeneous and Unbounded Time-Varying Delays , 2019, IEEE Transactions on Cybernetics.

[10]  Hua Wang,et al.  Image encryption based on synchronization of fractional chaotic systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

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

[12]  Zhigang Zeng,et al.  Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays , 2018, Neural Networks.

[13]  Song Zhu,et al.  Anti-synchronization of complex-valued memristor-based delayed neural networks , 2018, Neural Networks.

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

[15]  Song Zhu,et al.  Finite-Time Stability of Delayed Memristor-Based Fractional-Order Neural Networks , 2020, IEEE Transactions on Cybernetics.

[16]  Guoliang Chen,et al.  Extended dissipative analysis of generalized Markovian switching neural networks with two delay components , 2017, Neurocomputing.

[17]  Jinde Cao,et al.  Finite-time synchronization of fractional-order memristor-based neural networks with time delays , 2016, Neural Networks.

[18]  Zhigang Zeng,et al.  Synchronization regions of discrete-time dynamical networks with impulsive couplings , 2018, Inf. Sci..

[19]  Yanjun Shen,et al.  Finite-time synchronization control of a class of memristor-based recurrent neural networks , 2015, Neural Networks.

[20]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[21]  Jianwei Xia,et al.  Aperiodically Intermittent Control for Quasi-Synchronization of Delayed Memristive Neural Networks: An Interval Matrix and Matrix Measure Combined Method , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[22]  Yanchao Shi,et al.  Finite-time synchronization of stochastic memristor-based delayed neural networks , 2016, Neural Computing and Applications.

[23]  Chunyu Yang,et al.  Synchronization of Memristive Complex-Valued Neural Networks With Time Delays via Pinning Control Method , 2020, IEEE Transactions on Cybernetics.

[24]  Wenbo Wang,et al.  Finite-Time Stabilization for Stochastic Interval Systems with Time Delay and Application to Energy-Storing Electrical Circuits , 2019, Electronics.

[25]  Zhigang Zeng,et al.  Synchronization of Coupled Reaction–Diffusion Neural Networks With Directed Topology via an Adaptive Approach , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[26]  Zhidong Teng,et al.  Finite-time synchronization for memristor-based neural networks with time-varying delays , 2015, Neural Networks.

[27]  Zhigang Zeng,et al.  Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks , 2014, Neural Networks.

[28]  Lijuan Su,et al.  Exponential synchronization of memristor-based recurrent neural networks with multi-proportional delays , 2018, Neural Computing and Applications.

[29]  Shiping Wen,et al.  Quantized synchronization of memristive neural networks with time-varying delays via super-twisting algorithm , 2020, Neurocomputing.

[30]  Jing Zhang,et al.  Finite-Time Adaptive Fuzzy Control for Nonlinear Systems With Full State Constraints , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[31]  J. Tour,et al.  Electronics: The fourth element , 2008, Nature.

[32]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[33]  Jinde Cao,et al.  Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays , 2014, Cognitive Neurodynamics.

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

[35]  J. Aubin,et al.  Differential inclusions set-valued maps and viability theory , 1984 .

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

[37]  Gregory S. Snider,et al.  ‘Memristive’ switches enable ‘stateful’ logic operations via material implication , 2010, Nature.

[38]  F. Gao,et al.  Finite-time synchronization of memristor-based complex-valued neural networks with time delays , 2019, Physics Letters A.

[39]  Jinde Cao,et al.  Exponential Synchronization of Memristive Neural Networks With Delays: Interval Matrix Method , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[40]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[41]  R. Williams,et al.  How We Found The Missing Memristor , 2008, IEEE Spectrum.