Advertisement

Synchronization of Uncertain Chaotic System by Nonlinear Sliding Mode Method

  • Aijun Zhou
  • Guang Ren
  • ChengYong Shao
  • Yong Liang
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 206)

Abstract

A kind of variable gain nonlinear sliding mode adaptive method is proposed to solve the synchronization problem of chaotic systems with unknown parameters and uncertain functions. The design of nonlinear sliding mode is very skillful. It is not only make sliding surface stable but not make the control easy to be solved. Since with a constant gain, the control system will be not sensitive enough to small signals or it will be unstable to big signals. So the variable gain method is adopted to improve the control accuracy. At last, detailed numerical simulation is done to testify the rightness and effectiveness of the proposed method.

Keywords

Nonlinearity Sliding mode Chaos Synchronization Variable gain Uncertainty 

References

  1. 1.
    Roy R et al (1994) Experimental synchronization in laser chaos. Phys Rev Lett 72(22):3502–3505CrossRefGoogle Scholar
  2. 2.
    Sugawara T, Tachikawa M (1994) Observation of synchronization in laser chaos. Phys Rev Lett 72(22):3502–3506Google Scholar
  3. 3.
    Jing Gao Ping et al (2003) A simple global synchronization criterion for coupled chaotic systems. Chaos Solit Fract 3(15):925–935CrossRefGoogle Scholar
  4. 4.
    Yan Jianping, Li Changpin (2005) On synchronization of three chaotic systems. Chaos Solit Fract 32(23):1683–1688CrossRefMathSciNetGoogle Scholar
  5. 5.
    Sarasola, Torrealdea FJ, Anjou AD (2003) Feedback synchronization of chaotic systems. Int J Bifurcation Chaos 13(1):177–191Google Scholar
  6. 6.
    Yassen MT (2005) Chaos synchronization between two different chaotic systems using active control. Chaos Solit Fract 23(4):131–140CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Agiza HN, Yassen MT (2001) Synchronization of Rossler and Chen chaotic dynamical systems using active control. Phys Lett A 77(278):191–197CrossRefMathSciNetGoogle Scholar
  8. 8.
    Ho Ming-chung, Hung Yao-Chen (2002) Synchronization of two different systems by using generalized active control. Phys Lett A 4(301):424–428CrossRefMathSciNetGoogle Scholar
  9. 9.
    Jiang GP, Tang KS (2002) A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach. Int J Bifurcation Chaos 12(10):2239–2253CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Bu SL, Wang SQ (2002) An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems. Physica D 164:45–52CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Aijun Zhou
    • 1
  • Guang Ren
    • 1
  • ChengYong Shao
    • 2
  • Yong Liang
    • 3
  1. 1.Dalian Maritime UniversityDalianChina
  2. 2.Dalian Naval AcademyDalianChina
  3. 3.Naval Aeronautical and Astronautical UniversityYantaiChina

Personalised recommendations