Finite-time synchronization of delayed memristive neural networks via 1-norm-based analytical approach

By using 1-norm-based analytical approach, this paper considers finite-time (FET) synchronization for memristive neural networks (MNNs) with time-varying delays. New quantized controllers are designed, which can save communication channel and play an important role in synchronizing MNNs. By constructing Lyapunov function, and developing 1-norm-based analytical methods, several conditions are derived to guarantee that the MNNs can be synchronized within a settling time. In addition, the settling time is also presented for the considered MNNs. Some numerical simulations are provided to illustrate the theoretical results.

[1]  Lei Zhou,et al.  Synchronization of chaotic Lur'e systems with quantized sampled-data controller , 2014, Commun. Nonlinear Sci. Numer. Simul..

[2]  Xinsong Yang,et al.  Can neural networks with arbitrary delays be finite-timely synchronized? , 2014, Neurocomputing.

[3]  Yu Tang,et al.  Terminal sliding mode control for rigid robots , 1998, Autom..

[4]  Dong Yue,et al.  Quantized output feedback control for networked control systems , 2008, Inf. Sci..

[5]  Leon O. Chua,et al.  MEMRISTOR CELLULAR AUTOMATA AND MEMRISTOR DISCRETE-TIME CELLULAR NEURAL NETWORKS , 2009 .

[6]  Qiang Jia,et al.  Consensus of Multi-Agents With Event-Based Nonlinear Coupling Over Time-Varying Digraphs , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[8]  Fuad E. Alsaadi,et al.  Finite-Time Synchronization of Networks via Quantized Intermittent Pinning Control , 2018, IEEE Transactions on Cybernetics.

[9]  Frank C. Hoppensteadt,et al.  Pattern recognition via synchronization in phase-locked loop neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[10]  Chuandong Li,et al.  Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Jinde Cao,et al.  Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Wei Zhang,et al.  Synchronization of Memristor-Based Coupling Recurrent Neural Networks With Time-Varying Delays and Impulses , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[13]  S. Bhat,et al.  Finite-time stability of homogeneous systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[14]  Daniel W. C. Ho,et al.  Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach , 2016, IEEE Transactions on Cybernetics.

[15]  R. Rakkiyappan,et al.  Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[16]  Guodong Zhang,et al.  Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Lihua Xie,et al.  The sector bound approach to quantized feedback control , 2005, IEEE Transactions on Automatic Control.

[18]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[19]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Zhigang Zeng,et al.  Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays , 2012, Neural Networks.

[21]  U. Vincent,et al.  Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller , 2011 .

[22]  Qiang Jia,et al.  Event-Triggered Protocol for the Consensus of Multi-Agent Systems With State-Dependent Nonlinear Coupling , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[24]  Tingwen Huang,et al.  Passivity and Output Synchronization of Complex Dynamical Networks With Fixed and Adaptive Coupling Strength , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Jinde Cao,et al.  Finite-time synchronization of coupled neural networks via discontinuous controllers , 2011, Cognitive Neurodynamics.

[26]  Emilia Fridman,et al.  Comments on finite-time stability of time-delay systems , 2014, Autom..

[27]  Xinsong Yang,et al.  Finite-Time Synchronization of Coupled Networks With Markovian Topology and Impulsive Effects , 2016, IEEE Transactions on Automatic Control.

[28]  Mohammad Pourmahmood Aghababa,et al.  Synchronization of mechanical horizontal platform systems in finite time , 2012 .

[29]  V. Haimo.  Finite time controllers , 1986 .

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

[31]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[32]  Gang Feng,et al.  Synchronization of Complex Dynamical Networks With Time-Varying Delays Via Impulsive Distributed Control , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  M. P. Aghababa,et al.  Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique , 2011 .

[34]  Zhigang Zeng,et al.  Dynamic behaviors of memristor-based delayed recurrent networks , 2012, Neural Computing and Applications.

[35]  Guanrong Chen,et al.  Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback , 2009 .

[36]  Chuandong Li,et al.  Lag synchronization of hyperchaos with application to secure communications , 2005 .

[37]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

[38]  S H Strogatz,et al.  Coupled oscillators and biological synchronization. , 1993, Scientific American.

[39]  M. Forti,et al.  Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations , 2006 .

[40]  Yi Shen,et al.  Exponential synchronization of coupled memristive neural networks with time delays , 2013, Neural Computing and Applications.

[41]  A. Thomas,et al.  Memristor-based neural networks , 2013 .

[42]  Wei Zhang,et al.  Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control , 2018, Neural Networks.

[43]  Jacques M. Bahi,et al.  Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[44]  Kate Smith-Miles,et al.  A unified framework for chaotic neural-network approaches to combinatorial optimization , 1999, IEEE Trans. Neural Networks.

[45]  Jinde Cao,et al.  Finite-time synchronization of complex networks with nonidentical discontinuous nodes , 2013, Nonlinear Dynamics.

[46]  Lada A. Adamic,et al.  Internet: Growth dynamics of the World-Wide Web , 1999, Nature.