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Control of chaos in a piecewise smooth nonlinear system

Author

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  • Kousaka, Takuji
  • Ueta, Tetsushi
  • Ma, Yue
  • Kawakami, Hiroshi

Abstract

This paper shows the stabilization of the unstable periodic orbit of any given piecewise smooth system with linear and/or nonlinear characteristics. By utilizing the periodicity of the switching action, we construct the Poincaré mapping including all information of the original system. This mapping offers a first step toward extending a novel technique for controlling chaos based on the appropriate state feedback in piecewise smooth nonlinear systems. We also apply this approach to Rayleigh type oscillator described by the piecewise smooth nonlinear systems.

Suggested Citation

  • Kousaka, Takuji & Ueta, Tetsushi & Ma, Yue & Kawakami, Hiroshi, 2006. "Control of chaos in a piecewise smooth nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1019-1025.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:1019-1025
    DOI: 10.1016/j.chaos.2005.04.068
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    Cited by:

    1. Asemani, Mohammad Hassan & Majd, Vahid Johari, 2009. "Stability of output-feedback DPDC-based fuzzy synchronization of chaotic systems via LMI," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1126-1135.
    2. Chargé, Pascal & Fournier-Prunaret, Danièle & Guglielmi, Véronique, 2008. "Features analysis of a parametric PWL chaotic map and its utilization for secure transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1411-1422.
    3. Pan, Shing-Tai & Lai, Chih-Chin, 2008. "Identification of chaotic systems by neural network with hybrid learning algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 233-244.
    4. Brandon, Quentin & Ueta, Tetsushi & Fournier-Prunaret, Danièle & Kousaka, Takuji, 2009. "Numerical bifurcation analysis framework for autonomous piecewise-smooth dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 187-201.
    5. Miranda, Manuel & Alvarez, Joaquin, 2009. "Bifurcations and chaos produced by the modulation signal in a PWM buck converter," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2260-2271.

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