Skip to main content
SpringerLink
Log in

Robust adaptive backstepping synchronization for a class of uncertain chaotic systems using fuzzy disturbance observer

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper proposes a robust adaptive backstepping synchronization method for a class of uncertain chaotic systems. Unknown factors including system uncertainties and external disturbances are estimated by a fuzzy disturbance observer. By use of the fuzzy disturbance observer, any prior information about the unknown factors is not need. The proposed method using the estimated values guarantees the global synchronization for chaotic systems with mismatched uncertainties in the sense of uniform ultimate boundedness. Finally, numerical examples are presented to show the effectiveness of the method.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 5
Fig. 4
Fig. 6
Fig. 7

Similar content being viewed by others

References

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

    Article  MathSciNet  Google Scholar 

  2. Yang, T., Chua, L.O.: Secure communication via chaotic parameter modulation. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 43, 817–819 (1996)

    Article  Google Scholar 

  3. Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18, 141–148 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Sheikhan, M., Shahnazi, R., Garoucy, S.: Synchronization of general chaotic systems using neural controllers with application to secure communication. Neural Comput. Appl. (2011). doi:10.1007/s00521-011-0697-0

    Google Scholar 

  5. Meng, J., Wang, X.: Robust anti-synchronization of a class of delayed chaotic neural networks. Chaos 17, 023113 (2007)

    Article  MathSciNet  Google Scholar 

  6. Ji, D.H., Lee, D.W., Koo, J.H., Won, S.C., Lee, S.M., Park, Ju H.: Synchronization of neutral complex dynamical networks with coupling time varying delays. Nonlinear Dyn. 65(4), 349–358 (2011)

    Article  MathSciNet  Google Scholar 

  7. Strogatz, S.H.: Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life. Theia, an imprint of Hyperion, New York (2004)

    Google Scholar 

  8. Nijmeijer, H., Rodriguez-Angeles, A.: Synchronization of Mechanical Systems. World Scientific, Singapore (2003)

    Book  MATH  Google Scholar 

  9. Hu, G., Pivka, L., Zheleznyak, A.L.: Synchronization of a one-dimensional array of Chua’s circuits by feedback control and noise. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42, 736–740 (1995)

    Article  Google Scholar 

  10. Yu, H.T., Wong, Y.K., Chan, W.L., Tsang, K.M., Wang, J.: Feedback linearization control of chaos synchronization in coupled map-based neurons under external electrical stimulation. Int. J. Control. Autom. Syst. 9(5), 867–874 (2011)

    Article  Google Scholar 

  11. Su, W.J.: A global asymptotic synchronization problem via internal model approach. Int. J. Control. Autom. Syst. 8(5), 1153–1158 (2010)

    Article  Google Scholar 

  12. Jiang, G.-P., Chen, G., Tang, W.K.-S.: A new criterion for chaos synchronization using linear state feedback control. Int. J. Bifurc. Chaos 13, 2343–2351 (2003)

    Article  MATH  Google Scholar 

  13. Lee, S.M., Choi, S.J., Ji, D.H., Park, Ju H., Won, S.C.: Synchronization for chaotic Lur’e systems with sector restricted nonlinearities via delayed feedback control. Nonlinear Dyn. 59(1–2), 277–288 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Huang, L., Wang, M., Feng, R.: Parameters identification and adaptive synchronization of chaotic systems with unknown parameters. Phys. Lett. A 342, 299–304 (2005)

    Article  MATH  Google Scholar 

  15. Salarieh, H., Alasty, A.: Adaptive synchronization of two chaotic systems with stochastic unknown parameters. Commun. Nonlinear Sci. Numer. Simul. 14, 508–519 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, C., Ge, S.S.: Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos Solitons Fractals 12, 1199–1206 (2001)

    Article  MATH  Google Scholar 

  17. Wu, T., Chen, M.-S.: Chaos control of the modified Chua’s circuit system. Physica D 164, 53–58 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, J., Li, C., Zhang, H., Yu, J.: Chaos synchronization using single variable feedback based on backstepping method. Chaos Solitons Fractals 21, 1183–1193 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Bowong, S.: Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach. Nonlinear Dyn. 49, 59–70 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lin, D., Wang, X., Nian, F., Zhang, Y.: Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems. Neurocomputing 73, 2873–2881 (2010)

    Article  Google Scholar 

  21. Yau, H.-T., Yan, J.-J.: Chaos synchronization of different chaotic systems subjected to input nonlinearity. Appl. Math. Comput. 197, 775–788 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang, H., Han, Z.-Z., Xie, Q.-Y., Zhang, W.: Sliding mode control for chaotic systems based on LMI. Commun. Nonlinear Sci. Numer. Simul. 14, 1410–1417 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Mou, C., Jiang, C.-S., Bin, J., Wu, Q.-X.: Sliding mode synchronization controller design with neural network for uncertain chaotic systems. Chaos Solitons Fractals 39, 1856–1863 (2009)

    Article  MATH  Google Scholar 

  24. Park, J.H., Ji, D.H., Won, S.C., Lee, S.M.: \(\mathcal{H}_{\infty}\) synchronization of time-delayed chaotic systems. Appl. Math. Comput. 204, 170–177 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. Ahn, C.K., Jung, S.-T., Kang, S.-K., Joo, S.-C.: Adaptive \(\mathcal{H}_{\infty}\) synchronization for uncertain chaotic systems with external disturbance. Commun. Nonlinear Sci. Numer. Simul. 15, 2168–2177 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. Kuo, H.-H., Hou, Y.-Y., Yan, J.-J., Liao, T.-L.: Reliable synchronization of nonlinear chaotic systems. Math. Comput. Simul. 79, 1627–1635 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Grzybowski, J.M.V., Rafikov, M., Balthazar, J.M.: Synchronization of the unified chaotic system and application in secure communication. Commun. Nonlinear Sci. Numer. Simul. 14, 2793–2806 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Kim, E.: A fuzzy disturbance observer and its application to control. IEEE Trans. Fuzzy Syst. 10(1), 77–84 (2002)

    Article  Google Scholar 

  29. Kim, E., Park, C.: Fuzzy disturbance observer approach to robust tracking control of nonlinear sampled systems with the guaranteed suboptimal \(\mathcal{H}_{\infty}\) performance. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 34(3), 1574–1581 (2004)

    Article  Google Scholar 

  30. Yoo, W., Ji, D., Won, S.: Synchronization of two different non-autonomous chaotic systems using fuzzy disturbance observer. Phys. Lett. A 374, 1354–1361 (2010)

    Article  MATH  Google Scholar 

  31. Wang, L.X.: A Course in Fuzzy Systems and Control. Prentice-Hall PTR, Englewood Cliffs (1996)

    Google Scholar 

  32. Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  33. Khalil, H.K.: Nonlinear Systems. Prentice-Hall, Upper Saddle River (1996)

    Google Scholar 

Download references

Acknowledgements

The work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2010-0009373).

Author information

Authors and Affiliations

  1. Mobile Communication Division, Digital Media and Communications, Samsung Electronics, Co. Ltd., Maetan-dong, Suwon, Gyeonggi-do, 416-2, Korea

    D. H. Ji

  2. Department of Electrical Engineering, Pohang University of Science and Technology, San 31 Hyoja-Dong, Pohang, 790-784, Korea

    S. C. Jeong & S. C. Won

  3. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-dong, Kyongsan, 712-749, Republic of Korea

    Ju H. Park

Authors
  1. D. H. Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. C. Jeong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ju H. Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. C. Won
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ju H. Park.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ji, D.H., Jeong, S.C., Park, J.H. et al. Robust adaptive backstepping synchronization for a class of uncertain chaotic systems using fuzzy disturbance observer. Nonlinear Dyn 69, 1125–1136 (2012). https://doi.org/10.1007/s11071-012-0333-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-012-0333-2

Keywords

Search

Navigation