Almost sure synchronization control for stochastic delayed complex networks based on pinning adaptive method

This paper investigates the almost sure synchronization control problem for a class of stochastic delayed complex networks by using the stochastic differential equation theory and the Kronecker product technique. Different from the existing works, the considered problem is that all the nodes in the complex networks can synchronize with each other although the target node is unknown. Some sufficient conditions which guarantee the complex networks to have almost sure synchronization are derived and two kinds of controllers are designed, respectively. Finally, a numerical example is given to illustrate the effectiveness of the main results.

[1]  Daniel W. C. Ho,et al.  Globally Exponential Synchronization and Synchronizability for General Dynamical Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Shouming Zhong,et al.  Function projective synchronization in complex networks with switching topology and stochastic effects , 2015, Appl. Math. Comput..

[3]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[4]  Wu‐Hua Chen,et al.  H∞ synchronization for complex dynamical networks with coupling delays using distributed impulsive control , 2015 .

[5]  Xuerong Mao,et al.  Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching , 2008 .

[6]  Ji Xiang,et al.  Pinning Control of Uncertain Complex Networks to a Homogeneous Orbit , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Zhaoyan Wu,et al.  Adaptive pinning impulsive synchronization of dynamical networks with time-varying delay , 2015 .

[8]  Zhi-Hong Guan,et al.  Passive stability and synchronization of complex spatio-temporal switching networks with time delays , 2009, Autom..

[9]  Wenwu Yu,et al.  Distributed Adaptive Control of Synchronization in Complex Networks , 2012, IEEE Transactions on Automatic Control.

[10]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Jinde Cao,et al.  Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays , 2011 .

[12]  M. Bennett,et al.  Electrical Coupling and Neuronal Synchronization in the Mammalian Brain , 2004, Neuron.

[13]  Lei Wang,et al.  Exponential synchronization in complex networks with a single coupling delay , 2013, J. Frankl. Inst..

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

[15]  X. Mao,et al.  A note on the LaSalle-type theorems for stochastic differential delay equations , 2002 .

[16]  Fred C. Lee,et al.  Modeling of V2 Current-Mode Control , 2010, 2009 Twenty-Fourth Annual IEEE Applied Power Electronics Conference and Exposition.

[17]  Jinde Cao,et al.  Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays , 2010 .

[18]  R. Rakkiyappan,et al.  Stochastic sampled-data H∞ synchronization of coupled neutral-type delay partial differential systems , 2015, J. Frankl. Inst..

[19]  D. C. Dodder.  R-Matrix Analysis , 1976 .

[20]  G. Al-mahbashi,et al.  Adaptive projective lag synchronization of uncertain complex dynamical networks with delay coupling , 2015 .

[21]  Liangjian Hu,et al.  Almost sure exponential stabilisation of stochastic systems by state-feedback control , 2008, Autom..

[22]  Zhaoyan Wu,et al.  Impulsive pinning synchronization of discrete-time network , 2016 .

[23]  Wenxue Li,et al.  Outer synchronization of stochastic complex networks with time-varying delay , 2015 .

[24]  Jin Zhou,et al.  Pinning Complex Delayed Dynamical Networks by a Single Impulsive Controller , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  Jinde Cao,et al.  Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[26]  Tianping Chen,et al.  Global Synchronization of Discrete-Time Dynamical Network With a Directed Graph , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[27]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[28]  Zidong Wang,et al.  Bounded $H_{\infty}$ Synchronization and State Estimation for Discrete Time-Varying Stochastic Complex Networks Over a Finite Horizon , 2011, IEEE Transactions on Neural Networks.

[29]  M. Yahyazadeh,et al.  Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control. , 2011, ISA transactions.

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

[31]  Tingwen Huang,et al.  Passivity-based synchronization of a class of complex dynamical networks with time-varying delay , 2015, Autom..

[32]  Xiaodi Li,et al.  Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks , 2012, Fuzzy Sets Syst..

[33]  Wuneng Zhou,et al.  Mean square exponential synchronization in Lagrange sense for uncertain complex dynamical networks , 2012, J. Frankl. Inst..

[34]  Wai Keung Wong,et al.  Impulsive pinning synchronization of stochastic discrete-time networks , 2010, Neurocomputing.

[35]  S. Strogatz.  Exploring complex networks , 2001, Nature.

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