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Recursive backstepping control of chaotic Duffing oscillators

Author

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  • Harb, Ahmad M.
  • Zaher, Ashraf A.
  • Al-Qaisia, Ahmad A.
  • Zohdy, Mohammad A.

Abstract

In this paper, the dynamics of a forced Duffing oscillator is studied by means of modern nonlinear, bifurcation and chaos theories and shows that the system is ultimately experiencing chaos. The main objective is to characterize and control chaotic behavior. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Systematic following of a reference model is introduced. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally a discussion and conclusions are given with possible future extensions.

Suggested Citation

  • Harb, Ahmad M. & Zaher, Ashraf A. & Al-Qaisia, Ahmad A. & Zohdy, Mohammad A., 2007. "Recursive backstepping control of chaotic Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 639-645.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:639-645
    DOI: 10.1016/j.chaos.2006.03.119
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    Cited by:

    1. Farivar, Faezeh & Aliyari Shoorehdeli, Mahdi & Nekoui, Mohammad Ali & Teshnehlab, Mohammad, 2012. "Chaos control and generalized projective synchronization of heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive variable structure control," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 80-97.
    2. Farivar, Faezeh & Shoorehdeli, Mahdi Aliyari & Nekoui, Mohammad Ali & Teshnehlab, Mohammad, 2009. "Generalized projective synchronization for chaotic systems via Gaussian Radial Basis Adaptive Backstepping Control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 826-839.

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