Skip to main content

Sliding Mode Controller Design for the Global Chaos Synchronization of Coullet Systems

  • Conference paper

Abstract

In this paper, new results based on the sliding mode control are derived for the global chaos synchronization of identical Coullet chaotic systems (1981). The stability results for the sliding mode control based synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet chaotic systems. Numerical simulations are shown to illustrate the effectiveness of the sliding mode control results derived in this paper for the identical Coullet chaotic systems.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alligood, K.T., Sauer, T., Yorke, J.A.: Chaos: An Introduction to Dynamical Systems. Springer, New York (1997)

    Book  MATH  Google Scholar 

  2. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. Lakshmanan, M., Murali, K.: Chaos in Nonlinear Oscillators: Controlling and Synchronization. World Scientific, Singapore (1996)

    Book  MATH  Google Scholar 

  4. Han, S.K., Kerrer, C., Kuramoto, Y.: Dephasing and burstling in coupled neural oscillators. Phys. Rev. Lett. 75, 3190–3193 (1995)

    Article  Google Scholar 

  5. Blasius, B., Huppert, A., Stone, L.: Complex dynamics and phase synchronization in spatially extended ecological system. Nature 399, 354–359 (1999)

    Article  Google Scholar 

  6. Kwok, H.S., Wallace, K., Tang, S., Man, K.F.: Online secure communication system using chaotic map. Internat. J. Bifurcat. Chaos 14, 285–292 (2004)

    Article  MATH  Google Scholar 

  7. Kocarev, L., Parlitz, U.: General approach for chaos synchronization with applications to communications. Phys. Rev. Lett. 74, 5028–5030 (1995)

    Article  Google Scholar 

  8. Murali, K., Lakshmanan, M.: Secure communication using a compound signal using sampled-data feedback. Applied Math. Mech. 11, 1309–1315 (2003)

    Google Scholar 

  9. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ho, M.C., Hung, Y.C.: Synchronization of two different chaotic systems using generalized active network. Phys. Lett. A 301, 421–428 (2002)

    Article  MathSciNet  Google Scholar 

  11. Huang, L., Feng, R., Wang, M.: Synchronization of chaotic systems via nonlinear control. Phys. Lett. A 320, 271–275 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen, H.K.: Global chaos synchronization of new chaotic systems via nonlinear control. Chaos, Solit. Frac. 23, 1245–1251 (2005)

    Article  MATH  Google Scholar 

  13. Chen, S.H., Lü, J.: Synchronization of an uncertain unified system via adaptive control. Chaos, Solit. Frac. 14, 643–647 (2002)

    Article  MATH  Google Scholar 

  14. Lu, J., Han, X., Lü, J.: Adaptive feedback synchronization of a unified chaotic system. Phys. Lett. A 329, 327–333 (2004)

    Article  MATH  Google Scholar 

  15. Samuel, B.: Adaptive synchronization between two different chaotic dynamical systems. Adaptive Commun. Nonlinear Sci. Num. Simul. 12, 976–985 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Park, J.H., Kwon, O.M.: A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos, Solit. Fract. 17, 709–716 (2003)

    Article  MathSciNet  Google Scholar 

  17. Wu, X., Lü, J.: Parameter identification and backstepping control of uncertain Lü system. Chaos, Solit. Fract. 18, 721–729 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yu, Y.G., Zhang, S.C.: Adaptive backstepping synchronization of uncertain chaotic systems. Chaos, Solit. Fract. 27, 1369–1375 (2006)

    Article  Google Scholar 

  19. Yang, T., Chua, L.O.: Control of chaos using sampled-data feedback control. Internat. J. Bifurcat. Chaos 9, 215–219 (1999)

    Article  MathSciNet  Google Scholar 

  20. Zhao, J., Lu, J.: Using sampled-data feedback control and linear feedback synchronization in a new hyperchaotic system. Chaos, Solit. Fract. 35, 376–382 (2008)

    Article  Google Scholar 

  21. Slotine, J.E., Sastry, S.S.: Tracking control of nonlinear systems using sliding surface with application to robotic manipulators. Internat. J. Control 38, 465–492 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  22. Utkin, V.I.: Sliding mode control design principles and applications to electric drives. IEEE Trans. Industrial Electr. 40, 23–36 (1993)

    Article  Google Scholar 

  23. Saravanakumar, R., Vinoth Kumar, K., Ray, K.K.: Sliding mode control of induction motor using simulation approach. Internat. J. Control of Computer Science and Network Security 9, 93–104 (2009)

    Google Scholar 

  24. Arneodo, A., Coullet, P., Tresser, C.: Possible new strange attractors with spiral structure. Commun. Math. Phys. 79, 573–579 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  25. Hahn, W.: The Stability of Motion. Springer, New York (1967)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering

About this paper

Cite this paper

Vaidyanathan, S., Sampath, S. (2012). Sliding Mode Controller Design for the Global Chaos Synchronization of Coullet Systems. In: Meghanathan, N., Chaki, N., Nagamalai, D. (eds) Advances in Computer Science and Information Technology. Networks and Communications. CCSIT 2012. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27299-8_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27299-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27298-1

  • Online ISBN: 978-3-642-27299-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics