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Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach

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  • Dadras, Sara
  • Momeni, Hamid Reza

Abstract

An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio–Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio–Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3140-3146
    DOI: 10.1016/j.chaos.2009.04.018
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    References listed on IDEAS

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    1. Park, Ju H., 2007. "Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1552-1559.
    2. Chang, Wei-Der & Yan, Jun-Juh, 2005. "Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 167-175.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Park, Ju H., 2007. "Adaptive controller design for modified projective synchronization of Genesio–Tesi chaotic system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1154-1159.
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    Cited by:

    1. Zhang, Xuxi & Liu, Xianping & Zhu, Qidan, 2014. "Adaptive chatter free sliding mode control for a class of uncertain chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 431-435.
    2. 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.
    3. 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.

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