International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Backstepping Control and Synchronization for 4-D Lorenz-Stenflo Chaotic System with Single Input

  • Yu, Sung-Hun (School of Electrical and Electronic Engineering, Yonsei University) ;
  • Hyun, Chang-Ho (Division of Electrical Electronic and Control Engineering, Kongju National University) ;
  • Park, Mig-Non (School of Electrical and Electronic Engineering, Yonsei University)
  • Received : 2011.06.20
  • Accepted : 2011.09.08
  • Published : 2011.09.25
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Abstract

In this paper, a backstepping design is proposed to achieve stabilization and synchronization for the Lorenz-Stenflo (LS) chaotic system. The proposed method is a recursive Lyapunov-based scheme and provides a systematic procedure to design stabilizing controllers. The proposed controller enables stabilization of the chaotic motion and synchronization of two identical LS chaotic systems using only a single control input. Numerical simulations are presented to validate the proposed method.

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References

  1. E. Ott, C. Grebogi and J.A. Yorke, "Controlling chaos," Phys. Rev. Lett., vol.64, pp.1196-1199, 1990. https://doi.org/10.1103/PhysRevLett.64.1196
  2. L.M. Pecora and T.L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett., vol.64, pp.821-824, 1990. https://doi.org/10.1103/PhysRevLett.64.821
  3. T.L. Liao and S.H. Tsai, "Adaptive synchronization of chaotic systems and its application to secure communications," Chaos, Solitons & Fractals, vol.11, pp.1387-1396, 2000. https://doi.org/10.1016/S0960-0779(99)00051-X
  4. H.N. Agiza and M.T. Yassen, "Synchronization of Rossler and Chen dynamical systems using active control," Phys. Lett. A, vol.278, pp.191-197, 2001. https://doi.org/10.1016/S0375-9601(00)00777-5
  5. M. Jang, C. Chen and C. Chen, "Sliding mode control of hyperchaos in Rossler systems," Chaos Solitons & Fractals, vol.14, pp.1465-1476, 2002. https://doi.org/10.1016/S0960-0779(02)00084-X
  6. S. Sarasola, F.J. Torredea and A. D'anjou, "Feed-back synchronization of chaotic systems," Int. J. Bifurc. Chaos, vol.13, pp.177-191, 2003. https://doi.org/10.1142/S0218127403006443
  7. X. Liao, "Chaos synchronization of general Lur'e systems via time-delay feed-back control," Int. J. Bifurc. Chaos, vol.13, pp.207-213, 2003. https://doi.org/10.1142/S0218127403006455
  8. M.T. Yassen, "Chaos Synchronization between two different chaotic system using active control," Chaos, Solitons & Fractals, vol.23, pp.131-140, 2005. https://doi.org/10.1016/j.chaos.2004.03.038
  9. Y. Lei, W. Xu and W. Xie, "Synchronization of Two Chaotic Four-dimensional Systems using Active Control" Chaos, Solitons & Fractals, vol.32, no.5, pp.1823-1829, 2007. https://doi.org/10.1016/j.chaos.2005.12.014
  10. A. N. Njah and O. D. Sunday, "Synchronization of Identical and Non-identical 4-D Chaotic Systems via Lyapunov Direct Method," Chaos, International Journal of Nonlinear Science, vol.8, pp.3-10, 2009.
  11. R.A. Tang, Y.L. Liu and J.K. Xue, "An extended active control for chaos synchronization," Phys. Lett. A, vol.373, pp.1449-1454, 2009. https://doi.org/10.1016/j.physleta.2009.02.036
  12. M.T. Yassen, "Chaos Control of Chaotic Dynamical Systems using Backstepping Design", Chaos, Solitons & Fractals vol.27, no.2, pp.537-548, 2006. https://doi.org/10.1016/j.chaos.2005.03.046
  13. B. Wang and G.J. Wen, "On the synchronization of a class of chaotic systems based on backstepping method," Phys. Lett. A, vol.370, pp.35-39, 2007.. https://doi.org/10.1016/j.physleta.2007.05.030
  14. M. Krstic, I. Kanellakopoulus, P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley & sons, Inc., 1995.
  15. L. Stenflo "Generalized Lorenz Equations for Acoustic-Gravity Waves in the Atmosphere," Physica Scr, vol.53, pp.83-84, 1996. https://doi.org/10.1088/0031-8949/53/1/015

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