Decentralized adaptive synchronization of an uncertain complex delayed dynamical network

In this paper, we investigate the locally and globally adaptive synchronization problem for an uncertain complex dynamical network with time-varying coupling delays based on the decentralized control. The coupling terms here are bounded by high-order polynomials with known gains that are ubiquitous in a large class of complex dynamical networks. We generalize the usual technology of searching for an appropriate coordinates transformation to change the network dynamics into a series of decoupled lower-dimensional systems. Several adaptive synchronization criteria are derived by constructing the Lyapunov-Krasovskii functional and Barbalat lemma, and the proposed criteria are simple in form and convenient for the practical engineering design. Numerical simulations illustrated by a nearest-neighbor coupling network verify the effectiveness of the proposed synchronization scheme.

[1]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[2]  Chih-Chiang Cheng,et al.  A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems , 2003, IEEE Trans. Autom. Control..

[3]  Zhang Yi,et al.  Global synchronization of a class of delayed complex networks , 2006 .

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

[5]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[6]  Jinde Cao,et al.  Adaptive exponential synchronization of delayed chaotic networks , 2006 .

[7]  Guo-Ping Jiang,et al.  A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Jinde Cao,et al.  Synchronization in an array of linearly coupled networks with time-varying delay ☆ , 2006 .

[9]  Tianping Chen,et al.  Synchronization in general complex delayed dynamical networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Lada A. Adamic,et al.  Power-Law Distribution of the World Wide Web , 2000, Science.

[11]  P. Shi,et al.  Decentralized robust model reference adaptive control for interconnected time-delay systems , 2004, Proceedings of the 2004 American Control Conference.

[12]  Guanrong Chen,et al.  Robust adaptive synchronization of uncertain dynamical networks , 2004 .

[13]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[14]  Daizhan Cheng,et al.  Characterizing the synchronizability of small-world dynamical networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Guanrong Chen,et al.  Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint , 2003 .

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

[17]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[18]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .

[19]  Jinde Cao,et al.  Global synchronization in arrays of delayed neural networks with constant and delayed coupling , 2006 .

[20]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[21]  Mao-Yin Chen,et al.  Some Simple Synchronization Criteria for Complex Dynamical Networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[22]  B. Bollobás.  The evolution of random graphs , 1984 .

[23]  H. Nijmeijer,et al.  Cooperative oscillatory behavior of mutually coupled dynamical systems , 2001 .