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Nonlinear Dynamics

, Volume 69, Issue 1–2, pp 511–517 | Cite as

Modified projective synchronization of fractional-order chaotic systems via active sliding mode control

  • Xingyuan Wang
  • Xiaopeng Zhang
  • Chao Ma
Original Paper

Abstract

This paper is devoted to study the problem of modified projective synchronization of fractional-order chaotic system. Base on the stability theorems of fractional-order linear system, active sliding mode controller is proposed to synchronize two different fractional-order systems. Moreover, the controller is robust to the bounded noise. Numerical simulations are provided to show the effectiveness of the analytical results.

Keywords

Modified projective synchronization Chaotic fractional-order systems Active sliding mode control Bounded noise 

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References

  1. 1.
    Hartley, T.T., Lorenzo, C.F., Qammar, H.K.: Chaos in a fractional order Chua system. IEEE Trans. Circuits Syst. I 42(8), 485–490 (1996) CrossRefGoogle Scholar
  2. 2.
    Li, C.P., Deng, W.H.: Chaos synchronization of fractional-order differential systems. Int. J. Mod. Phys. B 20(7), 791–803 (2006) MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Li, C., Chen, G.: Chaos in the fractional order Chen system and its control. Chaos Solitons Fractals 22(3), 549–554 (2004) zbMATHCrossRefGoogle Scholar
  4. 4.
    Lu, J.: Chaotic dynamics of the fractional-order Lü system and its synchronization. Phys. Lett. A 354(4), 305–311 (2006) CrossRefGoogle Scholar
  5. 5.
    Li, C., Chen, G.: Chaos and hyperchaos in the fractional-order Rössler equations. Physica A 341(1), 55–61 (2004) MathSciNetCrossRefGoogle Scholar
  6. 6.
    Deng, W.H., Li, C.P.: Chaos synchronization of the fractional Lü system. Physica A 353(1), 61–72 (2005) CrossRefGoogle Scholar
  7. 7.
    Zhu, H., Zhou, S.B., Zhang, J.: Chaos and synchronization of the fractional-order Chua’s system. Chaos Solitons Fractals 39(4), 1595–1603 (2009) zbMATHCrossRefGoogle Scholar
  8. 8.
    Lu, J.: Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal. Chaos Solitons Fractals 27(2), 519–525 (2006) zbMATHCrossRefGoogle Scholar
  9. 9.
    Wang, X.Y., Song, J.M.: Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control. Commun. Nonlinear Sci. Numer. Simul. 14(8), 3351–3357 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Li, G.H.: Modified projective synchronization of chaotic system. Chaos Solitons Fractals 32(5), 1786–1790 (2007) MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Tang, Y., Fang, J.A.: General methods for modified projective synchronization of hyperchaotic systems with known or unknown parameters. Phys. Lett. A 372(11), 1816–1826 (2008) MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Park, J.H.: Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. J. Comput. Appl. Math. 213(1), 288–293 (2008) zbMATHCrossRefGoogle Scholar
  13. 13.
    Chen, L.P., Chai, Y., Wu, R.C.: Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems. Phys. Lett. A 375(21), 2099–2110 (2011) CrossRefGoogle Scholar
  14. 14.
    Huang, L.L., Xin, F., Wang, L.Y.: Circuit implementation and control of a new fractional-order hyperchaotic system. Acta Phys. Sin. 60(1), 010505 (2011) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Faculty of Electronic Information and Electrical EngineeringDalian University of TechnologyDalianChina

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