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Decentralized adaptive synchronization of an uncertain complex delayed dynamical network

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Abstract

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.

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Authors and Affiliations

  1. Key Laboratory Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang Liaoning, 110004, China

    Weisong Zhong & Jun Zhao

  2. Department of Information Engineering, The Australian National University, Canberra, ACT-0200, Australia

    Jun Zhao

  3. Department of Computer Engineering, Dogus University, Istanbul, TR-34722, Turkey

    Georgi M. Dimirovski

Authors
  1. Weisong Zhong
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  2. Jun Zhao
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  3. Georgi M. Dimirovski
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Corresponding author

Correspondence to Weisong Zhong.

Additional information

This work was supported by the National Natural Science Foundation of China (No.60574013, 60874024), the Australian Research Council, and Dogus University Fund for Science.

Weisong ZHONG is a Ph.D. candidate at Northeastern University. His research interests include passivity of nonlinear control systems with time delay, nonlinear robust and adaptive control, analysis and synthesis of complex dynamical networks, and constructive nonlinear control methods especially forwarding

Jun ZHAO received the Ph.D. in Control Theory and Applications in 1991 at Northeastern University, China. From 1992 to 1993, he was a postdoctoral fellow at the same university. Since 1994, he has been with School of Information Science and Engineering, Northeastern University, China, where he is currently a professor. From February 1998 to February 1999, he was a visiting scholar at the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign. He has held a research fellow position at the Department of Electronic Engineering, City University of Hong Kong. His main research interests include switched systems, nonlinear systems, geometric control theory, robust control, and complex networks.

Georgi M. DIMIROVSKI is with Dogus University, Department of Computer Engineering, Acibadem, Kadikoy, TR-34722, Istanbul, Republic of Turkey, and with SS Cyril and Methodius University, Faculty of Electrical and Computer Engineering, Skopje, Republic of Macedonia. He is an IEEE Senior Member and Foreign Member of the Academy of Engineering Sciences of Serbia. His main research interests include systems science and control, computational intelligence and soft computing, automation engineering, and human centered systems.

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Zhong, W., Zhao, J. & Dimirovski, G.M. Decentralized adaptive synchronization of an uncertain complex delayed dynamical network. J. Control Theory Appl. 7, 225–230 (2009). https://doi.org/10.1007/s11768-009-8032-3

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  • DOI: https://doi.org/10.1007/s11768-009-8032-3

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