Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 501843, 12 pages
http://dx.doi.org/10.1155/2012/501843
Research Article

Adaptive-Impulsive Control of the Projective Synchronization in Drive-Response Complex Dynamical Networks with Time-Varying Coupling

1School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang 310018, China
2Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 25 February 2011; Accepted 6 July 2011

Academic Editor: Zidong Wang

Copyright © 2012 Song Zheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. J. Watts and S. H. Strogatz, “Collective dynamics of ‘small-world’ networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998. View at Publisher · View at Google Scholar · View at Scopus
  2. A. -L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509–512, 1999. View at Publisher · View at Google Scholar
  3. C. W. Wu, Synchronization in Complex Networks of Nonlinear Dynamical Systems, World Scientific, Singapore, 2007.
  4. B. Shen, Z. Wang, and Y. S. Hung, “Distributed H-consensus filtering in sensor networks with multiple missing measurements: the finite-horizon case,” Automatica, vol. 46, no. 10, pp. 1682–1688, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Robust H fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 4, Article ID 5444946, pp. 712–725, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Dong, Z. Wang, and H. Gao, “Observer-based H control for systems with repeated scalar nonlinearities and multiple packet losses,” International Journal of Robust and Nonlinear Control, vol. 20, no. 12, pp. 1363–1378, 2010. View at Google Scholar · View at Zentralblatt MATH
  7. H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Variance-constrained H filtering for a class of nonlinear time-varying systems with multiple missing measurements: the finite-horizon case,” IEEE Transactions on Signal Processing, vol. 58, no. 5, pp. 2534–2543, 2010. View at Publisher · View at Google Scholar
  8. B. Shen, Z. Wang, Y. S. Hung, and G. Chesi, “Distributed H filtering for polynomial nonlinear stochastic systems in sensor networks,” IEEE Transactions on Industrial Electronics, vol. 58, no. 5, pp. 1971–1979, 2011. View at Publisher · View at Google Scholar
  9. B. Shen, Z. Wang, and X. Liu, “Bounded H synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon,” IEEE Transactions on Neural Networks, vol. 22, no. 1, pp. 145–157, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. P. De Lellis, M. di Bernardo, and F. Garofalo, “Synchronization of complex networks through local adaptive coupling,” Chaos, vol. 18, no. 3, Article ID 037110, 8 pages, 2008. View at Publisher · View at Google Scholar
  11. S. Wen, S. Chen, and W. Guo, “Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling,” Physics Letters A, vol. 372, no. 42, pp. 6340–6346, 2008. View at Publisher · View at Google Scholar
  12. S. Zheng, Q. Bi, and G. Cai, “Adaptive projective synchronization in complex networks with time-varying coupling delay,” Physics Letters A, vol. 373, no. 17, pp. 1553–1559, 2009. View at Publisher · View at Google Scholar
  13. X. F. Wang and G. Chen, “Pinning control of scale-free dynamical networks,” Physica A, vol. 310, no. 3-4, pp. 521–531, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. X. Li, X. Wang, and G. Chen, “Pinning a complex dynamical network to its equilibrium,” IEEE Transactions on Circuits and Systems, vol. 51, no. 10, pp. 2074–2087, 2004. View at Publisher · View at Google Scholar
  15. T. Chen, X. Liu, and W. Lu, “Pinning complex networks by a single controller,” IEEE Transactions on Circuits and Systems, vol. 54, no. 6, pp. 1317–1326, 2007. View at Publisher · View at Google Scholar
  16. W. Guo, F. Austin, S. Chen, and W. Sun, “Pinning synchronization of the complex networks with non-delayed and delayed coupling,” Physics Letters A, vol. 373, no. 17, pp. 1565–1572, 2009. View at Publisher · View at Google Scholar
  17. J. Zhou, L. Xiang, and Z. Liu, “Synchronization in complex delayed dynamical networks with impulsive effects,” Physica A, vol. 384, no. 2, pp. 684–692, 2007. View at Publisher · View at Google Scholar
  18. G. Zhang, Z. Liu, and Z. Ma, “Synchronization of complex dynamical networks via impulsive control,” Chaos, vol. 17, no. 4, Article ID 043126, 9 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. P. Li, J. Cao, and Z. Wang, “Robust impulsive synchronization of coupled delayed neural networks with uncertainties,” Physica A, vol. 373, pp. 261–272, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. Q. Song, J. Cao, and F. Liu, “Synchronization of complex dynamical networks with nonidentical nodes,” Physics Letters A, vol. 374, no. 4, pp. 544–551, 2010. View at Publisher · View at Google Scholar
  21. H. Jiang and Q. Bi, “Impulsive synchronization of networked nonlinear dynamical systems,” Physics Letters A, vol. 374, no. 27, pp. 2723–2729, 2010. View at Publisher · View at Google Scholar
  22. Y. Tang, S. Y. S. Leung, W. K. Wong, and J. A. Fang, “Impulsive pinning synchronization of stochastic discrete-time networks,” Neurocomputing, vol. 73, no. 10-12, pp. 2132–2139, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Yang, Y. W. Wang, H. O. Wang, K. Tanaka, and Z. H. Guan, “Delay independent synchronization of complex network via hybrid control,” in Proceedings of the American Control Conference (ACC '08), pp. 2266–2271, Seattle, Wash, USA, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. K. Li and C. H. Lai, “Adaptive-impulsive synchronization of uncertain complex dynamical networks,” Physics Letters A, vol. 372, no. 10, pp. 1601–1606, 2008. View at Publisher · View at Google Scholar
  25. H. B. Jiang, “Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical networks by the generalised Barbalat's lemma,” IET Control Theory & Applications, vol. 3, no. 10, pp. 1330–1340, 2009. View at Publisher · View at Google Scholar
  26. Z.-H. Guan, D. J. Hill, and J. Yao, “A hybrid impulsive and switching control strategy for synchronization of nonlinear systems and application to Chua's chaotic circuit,” International Journal of Bifurcation and Chaos, vol. 16, no. 1, pp. 229–238, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. R. Mainieri and J. Rehacek, “Projective synchronization in three-dimensional chaotic systems,” Physical Review Letters, vol. 82, no. 15, pp. 3042–3045, 1999. View at Publisher · View at Google Scholar · View at Scopus
  28. L. X. Guo, Z. Y. Xu, and M. F. Hu, “Projective synchronization in drive-response networks via impulsive control,” Chinese Physics Letters, vol. 25, no. 8, pp. 2816–2819, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. M. Hu, Y. Yang, Z. Xu, R. Zhang, and L. Guo, “Projective synchronization in drive-response dynamical networks,” Physica A, vol. 381, no. 1-2, pp. 457–466, 2007. View at Publisher · View at Google Scholar · View at Scopus
  30. Y. Zhao and Y. Yang, “The impulsive control synchronization of the drive-response complex system,” Physics Letters A, vol. 372, no. 48, pp. 7165–7171, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. M. Sun, C. Zeng, and L. Tian, “Projective synchronization in drive-response dynamical networks of partially linear systems with time-varying coupling delay,” Physics Letters A, vol. 372, no. 46, pp. 6904–6908, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. X. Xu, Y. Gao, Y. Zhao, and Y. Yang, “The impulsive control of the projective synchronization in the drive-response dynamical networks with coupling delay,” Advances in Neural Networks, vol. 6063, no. 1, pp. 520–527, 2010. View at Publisher · View at Google Scholar · View at Scopus
  33. J. Lü and G. Chen, “A time-varying complex dynamical network model and its controlled synchronization criteria,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 841–846, 2005. View at Publisher · View at Google Scholar
  34. M. Chen, “Synchronization in time-varying networks: a matrix measure approach,” Physical Review E, vol. 76, no. 1, Article ID 016104, 10 pages, 2007. View at Publisher · View at Google Scholar
  35. P. Li and Z. Yi, “Synchronization analysis of delayed complex networks with time-varying couplings,” Physica A, vol. 387, no. 14, pp. 3729–3737, 2008. View at Publisher · View at Google Scholar · View at Scopus