DOI QR코드

DOI QR Code

Control and Synchronization of New Hyperchaotic System using Active Backstepping Design

  • 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, Mi-Gnon (School of Electrical and Electronic Engineering, Yonsei University)
  • Received : 2011.03.16
  • Accepted : 2011.04.25
  • Published : 2011.06.25

Abstract

In this paper, an active backstepping design is proposed to achieve control and synchronization of a new hyperchaotic system. The proposed method is a systematic design approach and exists in a recursive procedure that interlaces the choice of a Lyapunov function with the design of the active control. The proposed controller enables stabilization of chaotic motion to the origin as well as synchronization of the two identical new hyperchaotic systems. Numerical simulations illustrate the validity of the proposed control technique.

Keywords

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. G. Perez and H.A. Cerdeira, "Extracting messages masked by chaos," Phys. Rev. Lett., vol. 74 pp. 1970-1973, 1995. https://doi.org/10.1103/PhysRevLett.74.1970
  4. L. Pecora, "Hyperchaos harnessed," World, vol. 9, pp. 17-18, 1996.
  5. 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
  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. 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.
  9. E.W. Bai and K.E. Lonngren, "Synchronization of two Lorenz systems using active control," Chaos, Solitons & Fractals, vol. 8, pp. 51-58, 1997. https://doi.org/10.1016/S0960-0779(96)00060-4
  10. 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
  11. 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
  12. U.E. Vincent, "Synchronization of identical and non-identical 4-D chaotic systems using active control," Chaos, Solitons & Fractals, vol. 37, pp. 1065-1075, 2008. https://doi.org/10.1016/j.chaos.2006.10.005
  13. 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
  14. X.H. Tan, T.Y. Zhang and Y.R. Yang, "Synchronizing chaotic systems using backstepping design," Chaos, Solitons & Fractals, vol. 16 pp. 37-45, 2003. https://doi.org/10.1016/S0960-0779(02)00153-4
  15. J. Zhang, C. Li, H. Zhang and Y. Yu, "Chaos synchronization using single variable feed-back based on backsepping method," Chaos, Solitons & Fractals, vol. 21, pp. 1183-1193, 2004. https://doi.org/10.1016/j.chaos.2003.12.079
  16. B. Wang and G.J. Wen, "On the synchronization of a class of chaotic systems based on backstepping method," Lett. A, vol. 370, pp. 35-39, 2007. https://doi.org/10.1016/j.physleta.2007.05.030
  17. A.N. Njah, K.S. Ojo, G.A. Adebayo and A.O. Obawole, "Generalized control and synchronization of chaos in RCL-shunted Josephson junction using backstepping design," Physica C, vol. 470, pp. 558-564, 2010. https://doi.org/10.1016/j.physc.2010.05.009
  18. Q. Jia, "Adaptive control and synchronization of a new hyperchaotic system with unknown parameters," Phys. Lett. A, vol. 362, pp. 424-429, 2007. https://doi.org/10.1016/j.physleta.2006.10.044
  19. H. Zhang, X.K. Ma, M. Li and J.L. Zou, "Controlling and tracking hyperchaotic Rossler system via active backstepping design," Chaos Solitons & Fractals, vol. 26, pp. 353-361, 2005. https://doi.org/10.1016/j.chaos.2004.12.032
  20. 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
  21. M. Krstic, I. Kanellakopoulus and P. Kokotovic, Nonlinear and adaptive control design, John Wiley & sons, Inc., 1995.
  22. G.Y. Qi, M.A. van Wyk, B.J. van Wyk and G.R. Chen, "On a new hyperchaotic system," Phys. Lett. A, vol. 372, pp. 124-136, 2008. https://doi.org/10.1016/j.physleta.2007.10.082
  23. G. Grassi, "Observer-based hyperchaos synchronization in cascaded discrete-time systems," Chaos, Solitons and Fractals, vol. 40, pp. 1029-1039, 2009. https://doi.org/10.1016/j.chaos.2007.08.060
  24. A.Y. Aguilar-Bustos and C. Cruz-Hernandez, "Synchronization of discrete-time hyperchaotic systems: an application in communications," Chaos, Solitons and Fractals, vol. 41, pp. 1301-1310, 2009. https://doi.org/10.1016/j.chaos.2008.05.012

Cited by

  1. Mathematical Modelling and Behavior Analysis of Addiction of Physical Exercise vol.24, pp.6, 2014, https://doi.org/10.5391/JKIIS.2014.24.6.615
  2. Observer-Based FL-SMC Active Damping for Back-to-Back PWM Converter with LCL Grid Filter vol.15, pp.3, 2015, https://doi.org/10.5391/IJFIS.2015.15.3.200
  3. Chaotic Behavior in a Dynamic Love Model with Different External Forces vol.15, pp.4, 2015, https://doi.org/10.5391/IJFIS.2015.15.4.283
  4. Behavior Analysis in Love Model of Romeo and Juliet with Time Delay vol.25, pp.2, 2015, https://doi.org/10.5391/JKIIS.2015.25.2.155
  5. Comparative Behavior Analysis in Love Model with Same and Different Time Delay vol.25, pp.3, 2015, https://doi.org/10.5391/JKIIS.2015.25.3.210
  6. Analysis of Nonlinear Dynamics in Family Model vol.25, pp.4, 2015, https://doi.org/10.5391/JKIIS.2015.25.4.313
  7. Analysis of Nonlinear Dynamics in Family Model including Parent-in-Law vol.26, pp.1, 2016, https://doi.org/10.5391/JKIIS.2016.26.1.037