Decentralized Synchronization and Output Tracking Control of Nondiffusively Coupled Complex Dynamical Networks

  • Gequn Liu
  • Xiaoming Xu
  • Lei Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6424)

Abstract

Diffusive coupling configuration of complex dynamical networks derives from the situation that nodes are coupled with states difference between each other. For the limitation of applicability of diffusive coupling model, it is necessary to study the control problem of nondiffusively coupled complex networks. A decentralized synchronization criterion with state feedback control scheme was proposed based on linear matrix inequality methodology. A simple criterion for the verification of decentralized stabilizability of the network is given. Furthermore, a decentralized output tracking control method is proposed based on the former synchronization criterion. Finally a nondiffusively coupled scale-free network is provided as the example to verify the effectiveness of the given methods.

Keywords

complex networks nondiffusive coupling synchronization control output tracking control linear matrix inequality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Boccaletti, S., Latora, V., Moreno, Y., et al.: Complex Networks: Structure and Dynamics. Physics Reports 424(4,5), 175–308 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Guo, L., Xu, X.: Complex networks. Shanghai Scientific & Technological Education Publishing House, Shanghai (2006)Google Scholar
  4. 4.
    Arenas, A., Guilera, A.D., Kurths, J., et al.: Synchronization in complex networks. Physics Reports 469, 93–153 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chen, G., Wang, X., Li, X., et al.: Some Recent Advances in Complex Networks Synchronization. In: Kyamakya, K. (ed.) Recent Advances in Nonlinear Dynamics and Synchronization, pp. 3–16. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Pecora, L.M., Carroll, T.L.: Master stability functions for synchronization coulped systems. Physical Review Letters 80(10), 2109–2112 (1998)CrossRefGoogle Scholar
  7. 7.
    Wang, X., Chen, G.: Pinning control of scale-free dynamical networks. Physica A 310, 521–531 (2002)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Duan, Z., Wang, J., Chen, G., et al.: Stability analysis and decentralized control of a class of complex dynamical networks. Automatica (44), 1028–1035 (2008)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Jamshidi, M., Chen, Z., Huang, C. (translated): Large-scale systems modeling and control. Science Press, Beijing (1986)Google Scholar
  10. 10.
    Wang, Y.: Large-scale systems—methodology and technology. Tianjin University Press, Tianjin (1993)Google Scholar
  11. 11.
    Siljak, D.D., Zecevic, A.I.: Control of large-scale systems: Beyond decentralized feedback. Annual Reviews in Control 29, 169–179 (2005)CrossRefMATHGoogle Scholar
  12. 12.
    Bakule, L.: Decentralized control: An overview. Annual Reviews in Control 32, 87–98 (2008)CrossRefGoogle Scholar
  13. 13.
    Zheng, W., Zhonghai, L., Siying, Z.: LMI approach of decentralized control and output tracking control for similar composite systems with mismatched interconnections. Control and Decision 15(4), 419–422 (2000)Google Scholar
  14. 14.
    Mao, C.-j., Yang, J.-h.: Decentralized Output Tracking for Linear Uncertain Interconnected Systems. Automatica 31(1), 151–154 (1995)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Boyd, S., Ghaoui, E., Feron, E., et al.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)CrossRefMATHGoogle Scholar
  16. 16.
    Yu, L.: Robust control—linear matrix inequality method. Tsinghua University Press, Beijing (2001)Google Scholar
  17. 17.
    Huang, H., Han, J.: Mathematical programming. Tsinghua University Press, Beijing (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gequn Liu
    • 1
    • 2
  • Xiaoming Xu
    • 1
    • 2
    • 3
  • Lei Liu
    • 1
  1. 1.School of ManagementUniversity of Shanghai for Science and TechnologyShanghaiChina
  2. 2.Shanghai Academy of Systems ScienceShanghaiChina
  3. 3.Department of AutomationShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations