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Model Reference Control of Hyperchaotic Systems

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  • Pengfei Zhao
  • Cai Liu
  • Xuan Feng

Abstract

We have applied a famous engineering method, called model reference control, to control hyperchaos. We have proposed a general description of the hyperchaotic system and its reference system. By using the Lyapunov stability theorem, we have obtained the expression of the controller. Four examples for the both certain case and the uncertain case show that our method is very effective for controlling hyperchaotic systems with both certain parameters and uncertain parameters.

Suggested Citation

  • Pengfei Zhao & Cai Liu & Xuan Feng, 2012. "Model Reference Control of Hyperchaotic Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:252487
    DOI: 10.1155/2012/252487
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    References listed on IDEAS

    as
    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. Jiang, Guo-Ping & Zheng, Wei Xing, 2005. "An LMI criterion for linear-state-feedback based chaos synchronization of a class of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 437-443.
    3. Zhang, Hao & Ma, Xi-kui & Li, Ming & Zou, Jian-long, 2005. "Controlling and tracking hyperchaotic Rössler system via active backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 353-361.
    4. Pengfei Zhao & Cai Liu & Xuan Feng, 2012. "Model Reference Control for an Economic Growth Cycle Model," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, July.
    5. Pengfei Zhao & Cai Liu & Xuan Feng, 2012. "Model Reference Control for an Economic Growth Cycle Model," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Gao, Tiegang & Chen, Zengqiang, 2008. "Image encryption based on a new total shuffling algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 213-220.
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