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Robust anti-synchronization of uncertain chaotic systems based on multiple-kernel least squares support vector machine modeling

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  • Chen, Qiang
  • Ren, Xuemei
  • Na, Jing

Abstract

In this paper, we propose a robust anti-synchronization scheme based on multiple-kernel least squares support vector machine (MK-LSSVM) modeling for two uncertain chaotic systems. The multiple-kernel regression, which is a linear combination of basic kernels, is designed to approximate system uncertainties by constructing a multiple-kernel Lagrangian function and computing the corresponding regression parameters. Then, a robust feedback control based on MK-LSSVM modeling is presented and an improved update law is employed to estimate the unknown bound of the approximation error. The proposed control scheme can guarantee the asymptotic convergence of the anti-synchronization errors in the presence of system uncertainties and external disturbances. Numerical examples are provided to show the effectiveness of the proposed method.

Suggested Citation

  • Chen, Qiang & Ren, Xuemei & Na, Jing, 2011. "Robust anti-synchronization of uncertain chaotic systems based on multiple-kernel least squares support vector machine modeling," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1080-1088.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:12:p:1080-1088
    DOI: 10.1016/j.chaos.2011.09.001
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    References listed on IDEAS

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    1. Palaniyandi, P., 2009. "Controlling based method for modelling chaotic dynamical systems from time series," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 625-658.
    2. Lin, Chih-Min & Peng, Ya-Fu & Lin, Ming-Hung, 2009. "CMAC-based adaptive backstepping synchronization of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 981-988.
    3. Al-Sawalha, Ayman, 2009. "Chaos anti-synchronization of two non-identical chaotic systems with known or fully unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1926-1932.
    4. Elabbasy, E.M. & El-Dessoky, M.M., 2009. "Adaptive anti-synchronization of different chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2174-2180.
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