IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i4p1857-1862.html
   My bibliography  Save this article

Sliding mode control for uncertain new chaotic dynamical system

Author

Listed:
  • Dadras, Sara
  • Momeni, Hamid Reza
  • Majd, Vahid Johari

Abstract

This paper proposes a sliding mode control strategy for a new uncertain chaotic dynamical system (Liu system). Using the sliding mode control technique and based on Lyapunov stability theory, a sliding surface is determined and a robust control law is established which stabilizes the uncertain chaotic system. The chattering phenomenon, which is inherent in conventional switching-type sliding controllers, due to this control law is very small and is damped quickly. An illustrative simulation result is given to demonstrate the effectiveness of the proposed sliding mode control design.

Suggested Citation

  • Dadras, Sara & Momeni, Hamid Reza & Majd, Vahid Johari, 2009. "Sliding mode control for uncertain new chaotic dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1857-1862.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1857-1862
    DOI: 10.1016/j.chaos.2008.07.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790800341X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.07.054?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. Chang, Jen-Fuh & Hung, Meei-Ling & Yang, Yi-Sung & Liao, Teh-Lu & Yan, Jun-Juh, 2008. "Controlling chaos of the family of Rössler systems using sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 609-622.
    2. Chen, Bing & Liu, Xiaoping & Tong, Shaocheng, 2007. "Adaptive fuzzy approach to control unified chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1180-1187.
    3. Layeghi, Hamed & Arjmand, Mehdi Tabe & Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing periodic orbits of chaotic systems using fuzzy adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1125-1135.
    4. Mello, L.F. & Messias, M. & Braga, D.C., 2008. "Bifurcation analysis of a new Lorenz-like chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1244-1255.
    5. Haeri, Mohammad & Tavazoei, Mohammad Saleh & Naseh, Majid Reza, 2007. "Synchronization of uncertain chaotic systems using active sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1230-1239.
    6. Yau, Her-Terng & Chen, Chieh-Li, 2006. "Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 709-718.
    7. Bonakdar, Mohammad & Samadi, Mostafa & Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincaré map," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 682-693.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dadras, Sara & Momeni, Hamid Reza, 2010. "Adaptive sliding mode control of chaotic dynamical systems with application to synchronization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2245-2257.
    2. Runzi Luo & Jiaojiao Fu & Haipeng Su, 2019. "The Exponential Stabilization of a Class of n-D Chaotic Systems via the Exact Solution Method," Complexity, Hindawi, vol. 2019, pages 1-7, May.
    3. Takhi, Hocine & Kemih, Karim & Moysis, Lazaros & Volos, Christos, 2021. "Passivity based sliding mode control and synchronization of a perturbed uncertain unified chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 150-169.

    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. Dadras, Sara & Momeni, Hamid Reza, 2009. "Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3140-3146.
    2. Poursamad, Amir & Markazi, Amir H.D., 2009. "Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3100-3109.
    3. Jin, Maolin & Chang, Pyung Hun, 2009. "Simple robust technique using time delay estimation for the control and synchronization of Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2672-2680.
    4. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive control of chaotic systems with stochastic time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 168-177.
    5. Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in an economic model via minimum entropy strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 839-847.
    6. Coelho, Leandro dos Santos & Araujo, Ernesto, 2009. "Identification of the Hénon chaotic map by fuzzy modeling and Nelder–Mead simplex method," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2762-2772.
    7. dos Santos Coelho, Leandro & Coelho, Antonio Augusto Rodrigues, 2009. "Model-free adaptive control optimization using a chaotic particle swarm approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2001-2009.
    8. Cheng, Chun-Kai & Kuo, Hang-Hong & Hou, Yi-You & Hwang, Chi-Chuan & Liao, Teh-Lu, 2008. "Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3093-3102.
    9. Peng, Ya-Fu, 2009. "Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 150-167.
    10. Zelinka, Ivan & Senkerik, Roman & Navratil, Eduard, 2009. "Investigation on evolutionary optimization of chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 111-129.
    11. Yi-You Hou, 2015. "Robust chaos synchronisation for a class of disturbed Rössler systems with multiple time-delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 1909-1916, August.
    12. Wang, Jiang & Si, Wenjie & Li, Huiyan, 2009. "Robust ISS-satisficing variable universe indirect fuzzy control for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 28-38.
    13. Belokolos, E.D. & Kharchenko, V.O. & Kharchenko, D.O., 2009. "Chaos in a generalized Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2595-2605.
    14. Tsai, Shun-Hung & Li, Tzuu-Hseng S., 2009. "Robust fuzzy control of a class of fuzzy bilinear systems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2028-2040.
    15. Hallaji, Majid & Dideban, Abbas & Khanesar, Mojtaba Ahmadieh & kamyad, Ali vahidyan, 2018. "Optimal synchronization of non-smooth fractional order chaotic systems with uncertainty based on extension of a numerical approach in fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 325-340.
    16. Peng, Ya-Fu, 2009. "Robust intelligent backstepping tracking control for uncertain non-linear chaotic systems using H∞ control technique," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2081-2096.
    17. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2008. "Synchronization of chaotic fractional-order systems via active sliding mode controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 57-70.
    18. Yao, Qijia, 2021. "Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    19. Zhang, Xiaohong & Khadra, Anmar & Yang, Dan & Li, Dong, 2009. "Analysis and design for unified exponential stability of three different impulsive T–S fuzzy systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1559-1566.
    20. Zhao, Yang & Wang, Wei, 2009. "Chaos synchronization in a Josephson junction system via active sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 60-66.

    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:41:y:2009:i:4:p:1857-1862. 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.