Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 521549, 11 pages
http://dx.doi.org/10.1155/2011/521549
Research Article

An Adaptive Tracking Control of Fractional-Order Chaotic Systems with Uncertain System Parameter

Ping Zhou1,2 and Rui Ding1,2

1Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 19 April 2011; Revised 22 August 2011; Accepted 22 September 2011

Academic Editor: J. Rodellar

Copyright © 2011 Ping Zhou and Rui Ding. 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. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, no. 11, pp. 1196–1199, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications, vol. 24 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific, River Edge, NJ, USA, 1998.
  4. X. Wu and Y. Lu, “Generalized projective synchronization of the fractional-order Chen hyperchaotic system,” Nonlinear Dynamics, vol. 57, no. 1-2, pp. 25–35, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. X. Wu and H. Wang, “A new chaotic system with fractional order and its projective synchronization,” Nonlinear Dynamics, vol. 61, no. 3, pp. 407–417, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Z. M. Odibat, “Adaptive feedback control and synchronization of non-identical chaotic fractional order systems,” Nonlinear Dynamics, vol. 60, no. 4, pp. 479–487, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Q. Zhu and J. Cao, “Adaptive synchronization of chaotic Cohen-Crossberg neural networks with mixed time delays,” Nonlinear Dynamics, vol. 61, no. 3, pp. 517–534, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. H. Salarieh and A. Alasty, “Adaptive synchronization of two chaotic systems with stochastic unknown parameters,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 508–519, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  9. X. Wang and M. Wang, “Adaptive robust synchronization for a class of different uncertain chaotic systems,” International Journal of Modern Physics B, vol. 22, no. 23, pp. 4069–4082, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. M. T. Yassen, “Controlling, synchronization and tracking chaotic Liu system using active backstepping design,” Physics Letters A, vol. 360, no. 4-5, pp. 582–587, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. X. Wang and Q. Zhao, “Tracking control and synchronization of two coupled neurons,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 849–855, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. T. L. Carroll, I. Triandaf, I. Schwartz, and L. Pecora, “Tracking unstable orbits in an experiment,” Physical Review A, vol. 46, no. 10, pp. 6189–6192, 1992. View at Publisher · View at Google Scholar · View at Scopus
  13. Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, “Tracking unstable steady states: extending the stability regime of a multimode laser system,” Physical Review Letters, vol. 69, no. 22, pp. 3169–3172, 1992. View at Publisher · View at Google Scholar · View at Scopus
  14. N. Noroozi, M. Roopaei, P. Karimaghaee, and A. A. Safavi, “Simple adaptive variable structure control for unknown chaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 3, pp. 707–727, 2010. View at Publisher · View at Google Scholar
  15. E. J. Hwang, C. H. Hyun, E. Kim, and M. Park, “Fuzzy model based adaptive synchronization of uncertain chaotic systems: robust tracking control approach,” Physics Letters A, vol. 373, no. 22, pp. 1935–1939, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Zhang and G. Feng, “Output tracking and synchronization of chaotic Chua's circuit with disturbances via model predictive regulator,” Chaos, Solitons and Fractals, vol. 39, no. 2, pp. 810–820, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. X. Li, W. Xu, and Y. Xiao, “Adaptive tracking control of a class of uncertain chaotic systems in the presence of random perturbations,” Journal of Sound and Vibration, vol. 314, no. 3–5, pp. 526–535, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. F. H. Min, Y. Yu, and C. J. Ge, “Circuit implementation and tracking control of the fractional-order hyper-chaotic Lü system,” Acta Physica Sinica, vol. 58, no. 3, pp. 1456–1461, 2009. View at Google Scholar · View at Scopus
  19. L. D. Zhao, J. B. Hu, and X. H. Liu, “Adaptive tracking control and synchronization of fractional hyper-chaotic Lorenz system with unknown parameters,” Acta Physica Sinica, vol. 59, no. 4, pp. 2305–2309, 2010. View at Google Scholar · View at Scopus
  20. D. Matignon, “Stability results on fractional differential equations with applications to control processing,” in IEEE Conference on Computational Engineering in Systems Applacations, pp. 963–968, Lille, France, 1996.
  21. I. Grigorenko and E. Grigorenko, “Chaotic dynamics of the fractional Lorenz system,” Physical Review Letters, vol. 91, no. 3, Article ID 034101, 4 pages, 2003. View at Google Scholar
  22. L.-J. Sheu, H.-K. Chen, J.-H. Chen, and L.-M. Tam, “Chaos in a new system with fractional order,” Chaos, Solitons and Fractals, vol. 31, no. 5, pp. 1203–1212, 2007. View at Publisher · View at Google Scholar
  23. C.-M. Chang and H.-K. Chen, “Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems,” Nonlinear Dynamics, vol. 62, no. 4, pp. 851–858, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH