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Generalized projective synchronization for chaotic systems via Gaussian Radial Basis Adaptive Backstepping Control

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  • Farivar, Faezeh
  • Shoorehdeli, Mahdi Aliyari
  • Nekoui, Mohammad Ali
  • Teshnehlab, Mohammad

Abstract

This paper proposes the generalized projective synchronization for chaotic systems via Gaussian Radial Basis Adaptive Backstepping Control. In the neural backstepping controller, a Gaussian radial basis function is utilized to on-line estimate the system dynamic function. The adaptation laws of the control system are derived in the sense of Lyapunov function, thus the system can be guaranteed to be asymptotically stable.

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  • Farivar, Faezeh & Shoorehdeli, Mahdi Aliyari & Nekoui, Mohammad Ali & Teshnehlab, Mohammad, 2009. "Generalized projective synchronization for chaotic systems via Gaussian Radial Basis Adaptive Backstepping Control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 826-839.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:826-839
    DOI: 10.1016/j.chaos.2009.02.012
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    References listed on IDEAS

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    1. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
    2. Yan, Jianping & Li, Changpin, 2005. "Generalized projective synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1119-1124.
    3. Harb, Ahmad M. & Zaher, Ashraf A. & Al-Qaisia, Ahmad A. & Zohdy, Mohammad A., 2007. "Recursive backstepping control of chaotic Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 639-645.
    4. Wen, Guilin & Xu, Daolin, 2005. "Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 71-77.
    5. Feng, Jianwen & Xu, Chen & Tang, Jianliang, 2007. "Controlling Chen’s chaotic attractor using two different techniques based on parameter identification," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1413-1418.
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    Cited by:

    1. Farivar, Faezeh & Aliyari Shoorehdeli, Mahdi & Nekoui, Mohammad Ali & Teshnehlab, Mohammad, 2012. "Chaos control and generalized projective synchronization of heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive variable structure control," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 80-97.
    2. Pal, Pikaso & Mukherjee, V. & Alemayehu, Hinsermu & Jin, Gang Gyoo & Feyisa, Gosa, 2021. "Generalized adaptive backstepping sliding mode control for synchronizing chaotic systems with uncertainties and disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 793-807.

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