Pinning impulsive stabilization of nonlinear Dynamical Networks with Time-Varying Delay

In this paper, a new impulsive control strategy, namely pinning impulsive control, is proposed for the stabilization problem of nonlinear dynamical networks with time-varying delay. In this strategy, only a small fraction of nodes is impulsively controlled to globally exponentially stabilize the whole dynamical network. By employing the Lyapunov method combined with the mathematical analysis approach as well as the comparison principle for impulsive systems, some criteria are obtained to guarantee the success of the global exponential stabilization process. The obtained criteria are closely related to the proportion of the controlled nodes, the impulsive strength, the impulsive interval and the time-delay. Numerical examples are given to demonstrate the effectiveness of the designed pinning impulsive controllers.

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

[2]  Youxian Sun,et al.  Adaptive synchronization of weighted complex dynamical networks through pinning , 2008 .

[3]  F. Garofalo,et al.  Controllability of complex networks via pinning. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  H. Kitano.  Systems Biology: A Brief Overview , 2002, Science.

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

[6]  J. Kurths,et al.  Enhancing complex-network synchronization , 2004, cond-mat/0406207.

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

[8]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[9]  Guanrong Chen,et al.  New criteria for synchronization stability of general complex dynamical networks with coupling delays , 2006 .

[10]  Jérôme Harmand,et al.  Further Results on Stabilization of Periodic Trajectories for a Chemostat With Two Species , 2008, IEEE Transactions on Automatic Control.

[11]  Yang Liu,et al.  Controllability for a Class of Linear Time-Varying Impulsive Systems With Time Delay in Control Input , 2011, IEEE Transactions on Automatic Control.

[12]  Xinzhi Liu,et al.  Robust impulsive synchronization of uncertain dynamical networks , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Jinde Cao,et al.  On periodic solutions of neural networks via differential inclusions , 2009, Neural Networks.

[14]  D. Ho,et al.  Stabilization of complex dynamical networks with noise disturbance under performance constraint , 2011 .

[15]  Daniel W. C. Ho,et al.  Pinning Stabilization of Linearly Coupled Stochastic Neural Networks via Minimum Number of Controllers , 2009, IEEE Transactions on Neural Networks.

[16]  Ligang Wu,et al.  Exponential stabilization of switched stochastic dynamical networks , 2009 .

[17]  JIANQUAN LU,et al.  Synchronization in an Array of Nonlinearly Coupled Chaotic Neural Networks with Delay Coupling , 2008, Int. J. Bifurc. Chaos.

[18]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[19]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[20]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[21]  C. Masoller,et al.  Synchronizability of chaotic logistic maps in delayed complex networks , 2008, 0805.2420.

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

[23]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[24]  Jürgen Kurths,et al.  Consensus over directed static networks with arbitrary finite communication delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Changsong Zhou,et al.  Universality in the synchronization of weighted random networks. , 2006, Physical review letters.

[26]  Ricard V. Solé,et al.  Self-Organization in Complex Ecosystems. (MPB-42) , 2006 .

[27]  方建安,et al.  Pinning impulsive synchronization of stochastic delayed coupled networks , 2011 .

[28]  C. K. Michael Tse,et al.  Adaptive Feedback Synchronization of a General Complex Dynamical Network With Delayed Nodes , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  M. Newman,et al.  Scaling and percolation in the small-world network model. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  Tao Yang,et al.  Impulsive Systems and Control: Theory and Applications , 2001 .

[31]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[32]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[33]  Jinde Cao,et al.  A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach , 2005 .

[34]  Guanrong Chen,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[36]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.

[37]  Jinde Cao,et al.  Global Synchronization in an Array of Delayed Neural Networks With Hybrid Coupling , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[38]  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.

[39]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[40]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

[41]  Ingo Fischer,et al.  Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication , 2000 .

[42]  Pablo M. Gleiser,et al.  Synchronization and structure in an adaptive oscillator network , 2006 .

[43]  Huaguang Zhang,et al.  Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[44]  Daoyi Xu,et al.  Stability Analysis and Design of Impulsive Control Systems With Time Delay , 2007, IEEE Transactions on Automatic Control.

[45]  Richard V. Solé,et al.  Self-Organization in Complex Ecosystems. , 2006 .