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Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters

Author

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  • Kim, Jae-Hun
  • Park, Chang-Woo
  • Kim, Euntai
  • Park, Mignon

Abstract

This paper presents a fuzzy model-based adaptive approach for synchronization of chaotic systems which consist of the drive and response systems. Takagi–Sugeno (T–S) fuzzy model is employed to represent the chaotic drive and response systems. Since the parameters of the drive system are assumed unknown, we design the response system that estimates the parameters of the drive system by adaptive strategy. The adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. In addition, the controller in the response system contains two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples, including Duffing oscillator and Lorenz attractor, are given to demonstrate the validity of the proposed adaptive synchronization approach.

Suggested Citation

  • Kim, Jae-Hun & Park, Chang-Woo & Kim, Euntai & Park, Mignon, 2005. "Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1353-1361.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:5:p:1353-1361
    DOI: 10.1016/j.chaos.2004.09.082
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    Cited by:

    1. Tutueva, Aleksandra & Moysis, Lazaros & Rybin, Vyacheslav & Zubarev, Alexander & Volos, Christos & Butusov, Denis, 2022. "Adaptive symmetry control in secure communication systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Feng, Yuhu & Hu, Liangjian, 2006. "On the quasi-controllability of continuous-time dynamic fuzzy control systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 177-188.
    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. Lee, Won-Ki & Hyun, Chang-Ho & Lee, Heejin & Kim, Euntai & Park, Mignon, 2007. "Model reference adaptive synchronization of T–S fuzzy discrete chaotic systems using output tracking control," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1590-1598.
    5. 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.
    6. Chang, Wei-Der, 2007. "Parameter identification of Chen and Lü systems: A differential evolution approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1469-1476.
    7. Coelho, Leandro dos Santos & Bernert, Diego Luis de Andrade, 2009. "PID control design for chaotic synchronization using a tribes optimization approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 634-640.
    8. Chang, Wei-Der, 2006. "Parameter identification of Rossler’s chaotic system by an evolutionary algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1047-1053.
    9. 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.
    10. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
    11. Chen, Chung-Cheng & Hsu, Chao-Hsing & Chen, Ying-Jen & Lin, Yen-Feng, 2007. "Disturbance attenuation of nonlinear control systems using an observer-based fuzzy feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 885-900.

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