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Chaos control in uncertain dynamical systems using nonlinear delayed feedback

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  • Salarieh, Hassan
  • Alasty, Aria

Abstract

In this paper based on the sliding mode concept, a nonlinear delayed feedback control is proposed for stabilizing the unstable periodic orbits (UPOs) of chaotic systems. It is assumed that the period of the desired UPO is known, but its time series and the initial conditions generated the UPO are not available. The ability of the proposed control method in stabilizing the UPO of the chaotic systems is analytically proved and the effectiveness of the method is numerically examined by applying it to the chaotic Duffing system.

Suggested Citation

  • Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in uncertain dynamical systems using nonlinear delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 67-71.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:67-71
    DOI: 10.1016/j.chaos.2007.11.007
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    References listed on IDEAS

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    1. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
    2. Alasty, Aria & Salarieh, Hassan, 2007. "Nonlinear feedback control of chaotic pendulum in presence of saturation effect," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 292-304.
    3. Nazzal, Jamal M. & Natsheh, Ammar N., 2007. "Chaos control using sliding-mode theory," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 695-702.
    4. Mohammad Shahrokhi, 2011. "Adaptive Control of Chaos," Chapters, in: Esteban Tlelo-Cuautle (ed.), Chaotic Systems, IntechOpen.
    5. Salarieh, Hassan & Shahrokhi, Mohammad, 2007. "Indirect adaptive control of discrete chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1188-1201.
    6. Alasty, Aria & Salarieh, Hassan, 2005. "Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 379-392.
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