Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis.

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

[2]  Xiaodi Li,et al.  Impulsive Control for Existence, Uniqueness, and Global Stability of Periodic Solutions of Recurrent Neural Networks With Discrete and Continuously Distributed Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

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

[4]  Yongduan Song,et al.  Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems , 2015, Autom..

[5]  M. P. Aghababa,et al.  A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs , 2012 .

[6]  Tingwen Huang,et al.  High-Performance Consensus Control in Networked Systems With Limited Bandwidth Communication and Time-Varying Directed Topologies , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Jinde Cao,et al.  Finite-time stochastic synchronization of complex networks , 2010 .

[8]  Jinde Cao,et al.  Synchronization of Markovian Coupled Neural Networks With Nonidentical Node-Delays and Random Coupling Strengths , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Shihua Li,et al.  Finite-Time Attitude Tracking Control of Spacecraft With Application to Attitude Synchronization , 2011, IEEE Transactions on Automatic Control.

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

[11]  Xiaodi Li,et al.  Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays , 2015, Inf. Sci..

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

[13]  Daniel W. C. Ho,et al.  Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control , 2014, Cognitive Neurodynamics.

[14]  Wilfrid Perruquetti,et al.  Finite-time stability and stabilization of time-delay systems , 2008, Syst. Control. Lett..

[15]  Jinde Cao,et al.  Exponential Synchronization of Delayed Neural Networks With Discontinuous Activations , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

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

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

[19]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[20]  Xinghuo Yu,et al.  Distributed Optimal Consensus Over Resource Allocation Network and Its Application to Dynamical Economic Dispatch , 2018, IEEE Transactions on Neural Networks and Learning Systems.

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

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

[23]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[24]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

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

[26]  Wei Zhang,et al.  Finite-time synchronization of uncertain unified chaotic systems based on CLF☆ , 2009 .

[27]  Xinzhi Liu,et al.  Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations , 2012, Inf. Sci..

[28]  Jinde Cao,et al.  A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks , 2014, Neural Networks.

[29]  Quan Yin,et al.  Adaptive Synchronization of Memristor-Based Neural Networks with Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Wenwu Yu,et al.  Impulsive synchronization schemes of stochastic complex networks with switching topology: Average time approach , 2014, Neural Networks.

[31]  Jinde Cao,et al.  Robust State Estimation for Neural Networks With Discontinuous Activations , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

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

[34]  Tingwen Huang,et al.  Event-Triggered Distributed Average Consensus Over Directed Digital Networks With Limited Communication Bandwidth , 2016, IEEE Transactions on Cybernetics.

[35]  Chaojie Li,et al.  Parallel and Distributed Computation for Dynamical Economic Dispatch , 2017, IEEE Transactions on Smart Grid.

[36]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

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

[38]  Tianping Chen,et al.  Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions , 2006, Neural Computation.

[39]  Gang Feng,et al.  Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems , 2012, Autom..

[40]  Daniel W. C. Ho,et al.  Finite-Time Cluster Synchronization of T–S Fuzzy Complex Networks With Discontinuous Subsystems and Random Coupling Delays , 2015, IEEE Transactions on Fuzzy Systems.

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

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

[43]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[44]  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..

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

[46]  Jinde Cao,et al.  Nonsmooth finite-time stabilization of neural networks with discontinuous activations , 2014, Neural Networks.