Adaptive Pinning Synchronization of Complex Networks with Stochastic Perturbations

The adaptive pinning synchronization is investigated for complex networks with nondelayed and delayed couplings and vector-form stochastic perturbations. Two kinds of adaptive pinning controllers are designed. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are developed to guarantee the synchronization of the proposed complex networks even if partial states of the nodes are coupled. Furthermore, three examples with their numerical simulations are employed to show the effectiveness of the theoretical results.

[1]  Zidong Wang,et al.  Global Synchronization Control of General Delayed Discrete-Time Networks With Stochastic Coupling and Disturbances , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[3]  Jinde Cao,et al.  Pinning synchronization of delayed dynamical networks via periodically intermittent control. , 2009, Chaos.

[4]  Zengqiang Chen,et al.  Pinning control of complex dynamical networks with heterogeneous delays , 2008, Comput. Math. Appl..

[5]  Andrey Pototsky,et al.  Synchronization of a large number of continuous one-dimensional stochastic elements with time-delayed mean-field coupling , 2009 .

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

[7]  M. Small,et al.  Pinning synchronization of delayed neural networks. , 2008, Chaos.

[8]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[9]  Shihua Chen,et al.  Pinning synchronization of the complex networks with non-delayed and delayed coupling , 2009 .

[10]  Tianping Chen,et al.  Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay , 2006 .

[11]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[12]  Yonghui Sun,et al.  Synchronization in an array of linearly stochastically coupled networks with time delays , 2007 .

[13]  C. Wu.  On the relationship between pinning control effectiveness and graph topology in complex networks of dynamical systems. , 2008, Chaos.

[14]  Junan Lu,et al.  Pinning adaptive synchronization of a general complex dynamical network , 2008, Autom..

[15]  Jinde Cao,et al.  On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Jinde Cao,et al.  Synchronization in Arrays of Delay-Coupled Neural Networks via Adaptive Control , 2007, 2007 IEEE International Conference on Control and Automation.

[17]  Jin Zhou,et al.  Synchronization in complex delayed dynamical networks with impulsive effects , 2007 .

[18]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[19]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[20]  Tianping Chen,et al.  Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix , 2008 .

[21]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[22]  Donghua Zhou,et al.  Synchronization in uncertain complex networks. , 2006, Chaos.

[23]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[24]  Wei Ren.  Consensus Seeking in Multi-vehicle Systems with a Time-varying Reference State , 2007, 2007 American Control Conference.

[25]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.