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Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback

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  • Goharrizi, Amin Yazdanpanah
  • Khaki-Sedigh, Ali
  • Sepehri, Nariman

Abstract

A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.

Suggested Citation

  • Goharrizi, Amin Yazdanpanah & Khaki-Sedigh, Ali & Sepehri, Nariman, 2009. "Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2448-2455.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2448-2455
    DOI: 10.1016/j.chaos.2008.09.033
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    References listed on IDEAS

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    1. Khaki-Sedigh, A. & Yazdanpanah-Goharrizi, A., 2006. "Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1063-1072.
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    5. Cui, Bao Tong & Hua, Min Gang, 2006. "Robust passive control for uncertain discrete-time systems with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 331-341.
    6. Wang, Jiang & Zhang, Ting & Che, Yanqiu, 2007. "Chaos control and synchronization of two neurons exposed to ELF external electric field," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 839-850.
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