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Practical adaptive synchronization of a class of uncertain chaotic systems

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Abstract

This paper studies the practical adaptive synchronization of a class of uncertain chaotic systems in the drive-response framework. An adaptive response system is designed to practically synchronize a given drive chaotic system with uncertainties. An improved adaptation law on the upper bound of uncertainties is proposed to guarantee the boundedness of both the synchronization error and the estimated feedback coupling gains. The efficiency and effectiveness of the proposed approach is illustrated by computer simulation.

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References

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

    Article  MathSciNet  Google Scholar 

  2. Blekhman, I.I., Fradkov, A.L., Nijmeijer, H., Pogromsky, A.Y.: On self-synchronization and controlled synchronization. Syst. Control Lett. 31, 299–305 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cuomo, K.M., Oppenheim, A.V.: Circuit implementation of synchronized chaos with application to communication. Phys. Rev. Lett. 71, 65–68 (1993)

    Article  Google Scholar 

  4. Nijmeijer, H., Mareels, I.M.Y.: An observer looks at synchronization. IEEE Trans. Circuits Syst. I 44, 882–889 (1997)

    Article  MathSciNet  Google Scholar 

  5. Morgül, O., Solak, E.: Observer based synchronization of chaotic systems. Phys. Rev. E 54, 4803–4811 (1996)

    Article  Google Scholar 

  6. Grassi, G., Mascolo, S.: Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal. IEEE Trans. Circuits Syst. I 44, 1011–1013 (1997)

    Article  Google Scholar 

  7. Feki, M.: Observer-based exact synchronization of ideal and mismatched chaotic systems. Phys. Lett. A 309, 53–60 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bowong, S., Moukam Kakmeni, F.M., Koina, R.: A New synchronization principle for a class of Lur’e systems with applications in secure communications. Int. J. Bifur. Chaos 14, 2477–2491 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Femat, R., Alvarez-Ramirez, J., Fernandez-Anaya, G.: Adaptive synchronization of high-order chaotic systems: a feedback with low-order parametrization. Physica D 139, 231–246 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lian, K.Y., Liu, P., Chiang, T.S., Chiu, C.S.: Adaptive synchronization design for chaotic systems via a scalar driving signal. IEEE Trans. Circuits Syst. I 49, 17–27 (2002)

    Article  Google Scholar 

  11. Hong, Y.G., Qin, H.S., Chen, G.R.: Adaptive synchronization of chaotic systems via state or output feedback control. Int. J. Bifur. Chaos 11, 1149–1158 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Bowong, S., Moukam Kakmeni, F.M.: Synchronization of uncertain chaotic systems via backstepping approach. Chaos Solitons Fractals 21, 999–1011 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  13. Yang, T., Shao, H.H.: Synchronizing chaotic dynamics with uncertainties based on a sliding mode control design. Phys. Rev. E 65, 046210–046215 (2002)

    Article  Google Scholar 

  14. Li, Z., Shi, S.: Robust adaptive synchronization of Rössler and Chen chaotic systems via slide technique. Phys. Lett. A 311, 389–395 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Bowong, S., Moukam Kakmeni, F.M., Tchawoua, C.: Controlled synchronization of chaotic systems with uncertainties via a sliding mode control design. Phys. Rev. E 70, 066217–06622 (2004)

    Article  MathSciNet  Google Scholar 

  16. Yang, T., Chua, L.O.: Impulsive stabilization for control and synchronization of chaotic systems: Theory and application to secure communication. IEEE Trans. Circuits Syst. I Fund. Theor. Appl. 44, 976–988 (1997)

    Article  MathSciNet  Google Scholar 

  17. Chen, S., Yang, Q., Wang, C.: Impulsive control and synchronization of unified chaotic system. Chaos Solitons Fractals 20, 751–758 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Yu, X., Song, Y.X.: Chaos synchronization via controlling partial state of chaotic systems. Int. J. Bifur. Chaos 11, 1737–1741 (2001)

    Article  Google Scholar 

  19. Wang, X.F., Wang, Z.Q., Chen, G.: A new criterion for synchronization of coupled chaotic oscillators with application to Chua’s circuits. Int. J. Bifur. Chaos 9, 1169–1174 (1999)

    Article  Google Scholar 

  20. Grassi, G., Mascolo, S.: Synchronizing high dimensional chaotic systems via eigenvalue placement with application to cellular neural networks. Int. J. Bifur. Chaos 9, 705–711 (1999)

    Article  MATH  Google Scholar 

  21. Fang, J.Q., Hong, Y., Chen, G.: Switching manifold approach to chaos synchronization. Phys. Rev. E 59, R2523–R2536 (1999)

    Article  Google Scholar 

  22. Marino, R., Tomei, P.: Nonlinear Control Design-Geometric, Adaptive, Robust. Prentice-Hall, Englewood Cliffs (1995)

    Google Scholar 

  23. Hsu, K.C.: Sliding mode controllers for uncertain systems with input nonlinearity. J. Guid. Control Dyn. 21, 666–669 (1998)

    Article  Google Scholar 

  24. Yan, J.J.: Sliding mode control design for uncertain time-delay systems subjected to a class of nonlinear inputs. Int. J. Robust Nonlinear Control 13, 519–532 (2003)

    Article  MATH  Google Scholar 

  25. Corless, M.J., Leitmann, G.: Continuous state feedback guarantying uniform ultimate boundedness for uncertain dynamic system. IEEE Trans. Autom. Control 26, 1139–1144 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  26. Khalil, H.K.: Nonlinear Systems, 3rd edn. Springer, United Kingdom (1995)

    Google Scholar 

  27. Zhong, G.Q.: Implementation of Chua’s circuit with a cubic nonlinearity. Int. J. Bifur. Chaos 41, 934–941 (1994)

    Google Scholar 

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Authors and Affiliations

  1. Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon

    Samuel Bowong

  2. Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    Jean Jules Tewa

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  1. Samuel Bowong
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  2. Jean Jules Tewa
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Correspondence to Samuel Bowong.

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Bowong, S., Tewa, J.J. Practical adaptive synchronization of a class of uncertain chaotic systems. Nonlinear Dyn 56, 57–68 (2009). https://doi.org/10.1007/s11071-008-9379-6

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  • DOI: https://doi.org/10.1007/s11071-008-9379-6

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