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Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems

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  • Yau, Her-Terng
  • Chen, Chieh-Li

Abstract

This paper proposes a chattering-free fuzzy sliding-mode control (FSMC) strategy for uncertain chaotic systems. A fuzzy logic control is used to replace the discontinuous sign function of the reaching law in traditional sliding-mode control (SMC), and hence a control input without chattering is obtained in the chaotic systems with uncertainties. Base on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding-mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. The Genesio chaotic system is used to test the proposed control strategy and the simulation results show the FSMC not only can control the uncertain chaotic behaviors to a desired state without oscillator very fast, but also the switching function is smooth without chattering. This result implies that this strategy is feasible and effective for chaos control.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:3:p:709-718
    DOI: 10.1016/j.chaos.2006.03.077
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    1. N. Gershenfeld & B. Schoner & E. Metois, 1999. "Cluster-weighted modelling for time-series analysis," Nature, Nature, vol. 397(6717), pages 329-332, January.
    2. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Gao, Yuan & Liang, Chenghua & Wu, Qiqi & Yuan, Haiying, 2015. "A new fractional-order hyperchaotic system and its modified projective synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 190-204.
    8. 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.
    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. 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.
    11. 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.
    12. Kuo, Hang-Hong & Hou, Yi-You & Yan, Jun-Juh & Liao, Teh-Lu, 2009. "Reliable synchronization of nonlinear chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1627-1635.

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