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Combining dither smoothing technique and state feedback linearization to control undifferentiable chaotic systems

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  • Tsai, Hsun-Heng
  • Fuh, Chyun-Chau

Abstract

State feedback linearization is a crucial control approach for chaotic systems. However, the linearization method requires the dynamical equations to be sufficiently smooth. Consequently, inherent nonlinearities in the form of nondifferentiable functions are usually excluded when modeling the system in order to permit the use of the feedback linearization method. However, the resulting model mismatch causes the overall system to suffer from problems of control accuracy and closed-loop stability. These drawbacks may be overcome to a certain extent by the injection of an external signal, i.e. by applying the so-called dither smoothing technique. In this approach, the original inherent nonlinearities are modified (i.e. smoothed) by injecting a high-frequency signal, generating so-called equivalent nonlinearities in their place. In other words, the dither smoothing technique enables the state feedback linearization method to be applied to chaotic systems involving undifferentiable nonlinearities. This study presents the application of the dither smoothing technique to a chaotic circuit in order to demonstrate the proposed strategy.

Suggested Citation

  • Tsai, Hsun-Heng & Fuh, Chyun-Chau, 2007. "Combining dither smoothing technique and state feedback linearization to control undifferentiable chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 886-895.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:3:p:886-895
    DOI: 10.1016/j.chaos.2006.04.045
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    1. Chandrasekar, V.K. & Pandey, S.N. & Senthilvelan, M. & Lakshmanan, M., 2005. "Application of extended Prelle–Singer procedure to the generalized modified Emden type equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1399-1406.
    2. Ge, Zheng-Ming & Chang, Ching-Ming & Chen, Yen-Sheng, 2006. "Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1298-1315.
    3. Choudhury, S. Roy, 2006. "Painlevé analysis of nonlinear evolution equations—an algorithmic method," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 139-152.
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