Fixed-Time Stochastic Synchronization of Complex Networks via Continuous Control

This paper investigates the fixed-time synchronization (FDTS) of complex networks with stochastic perturbations. A new control scheme is designed to realize the synchronization goal. Moreover, the designed controller without sign function is continuous, which means the chattering phenomenon in some previous results can be avoided. By constructing Lyapunov functionals, using the properties of the Weiner process as well as applying a designed comparison system, several FDTS criteria are obtained. Synchronization criteria of this paper are very general and can be utilized in directed and undirected weighted networks. Numerical simulations are given to illustrate the theoretical results.

[1]  Chuandong Li,et al.  Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication , 2004 .

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

[3]  Qian Ma,et al.  Finite-time synchronization for complex dynamical networks with time-varying delays , 2012 .

[4]  Wenbing Zhang,et al.  Finite-time cluster synchronisation of Markovian switching complex networks with stochastic perturbations , 2014 .

[5]  Yang Tang,et al.  Synchronization of Stochastic Dynamical Networks Under Impulsive Control With Time Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Andrey Polyakov,et al.  Finite-time and fixed-time stabilization: Implicit Lyapunov function approach , 2015, Autom..

[7]  Guanrong Chen,et al.  Hybrid chaos synchronization and its application in information processing , 2002 .

[8]  Tianping Chen,et al.  A note on finite-time and fixed-time stability , 2015, Neural Networks.

[9]  Tianping Chen,et al.  Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control , 2018, IEEE Transactions on Cybernetics.

[10]  Wai Keung Wong,et al.  Stochastic Synchronization of Complex Networks With Mixed Impulses , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Jinde Cao,et al.  Synchronization of delayed complex dynamical networks with impulsive and stochastic effects , 2011 .

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

[13]  Jinde Cao,et al.  Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks , 2016, Neural Networks.

[14]  Yulong Xu,et al.  Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates , 2014, J. Frankl. Inst..

[15]  Zongyu Zuo,et al.  Distributed robust finite-time nonlinear consensus protocols for multi-agent systems , 2016, Int. J. Syst. Sci..

[16]  R. Rakkiyappan,et al.  Pinning sampled-data synchronization of complex dynamical networks with Markovian jumping and mixed delays using multiple integral approach , 2016, Complex..

[17]  Junmi Li,et al.  Stochastic synchronization for complex dynamical networks with time-varying couplings , 2015 .

[18]  Quanxin Zhu,et al.  Synchronization of reaction–diffusion neural networks with time-varying delays via stochastic sampled-data controller , 2014, Nonlinear Dynamics.

[19]  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.

[20]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

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

[22]  Zhidong Teng,et al.  Exponential Synchronization of Complex Networks With Finite Distributed Delays Coupling , 2011, IEEE Transactions on Neural Networks.

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

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

[25]  Tianping Chen,et al.  Fixed-time cluster synchronization for complex networks via pinning control , 2015, ArXiv.

[26]  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.

[27]  Ya Zhang,et al.  Global synchronization of stochastic delayed complex networks , 2012, Nonlinear Dynamics.

[28]  Jinde Cao,et al.  Stochastic synchronization of coupled neural networks with intermittent control , 2009 .

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

[30]  Huaguang Zhang,et al.  Synchronization stability in complex interconnected neural networks with nonsymmetric coupling , 2013, Neurocomputing.

[31]  James Lam,et al.  Fixed-Time Synchronization of Complex Networks With Impulsive Effects via Nonchattering Control , 2017, IEEE Transactions on Automatic Control.