IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i3p886-895.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906003742
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.04.045?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Zheng & Chau, K.T., 2008. "Anti-control of chaos of a permanent magnet DC motor system for vibratory compactors," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 694-708.
    2. Zribi, Mohamed & Oteafy, Ahmed & Smaoui, Nejib, 2009. "Controlling chaos in the permanent magnet synchronous motor," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1266-1276.
    3. Giné, Jaume, 2007. "On some open problems in planar differential systems and Hilbert’s 16th problem," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1118-1134.
    4. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2008. "Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 592-604.
    5. Chen, Juhn-Horng & Chen, Hsien-Keng & Lin, Yu-Kai, 2009. "Synchronization and anti-synchronization coexist in Chen–Lee chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 707-716.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:34:y:2007:i:3:p:886-895. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.