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Adaptive set-point tracking of the Lorenz chaotic system using non-linear feedback

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  • Haghighatdar, F.
  • Ataei, M.

Abstract

In this paper, an adaptive control method for set-point tracking of the Lorenz chaotic system by using non-linear feedback is proposed. The design procedure of the proposed controller is accomplished in two steps. At the first step, using Lyapunov’s direct method, a non-linear state feedback is selected so that without any need to apply identification techniques, in despite of the uncertain parameters existence in the system state equations, the asymptotic stability of the general Lorenz system is guaranteed in a stochastic point of the manifold containing general system equilibrium points. At the second step, a linear state feedback with adaptive gain is added to the prior controller to eliminate the tracking error. In order to guarantee the system asymptotic stability at desired set-point, the indirect Lyapunov’s method is used. Finally, to show the effectiveness of the proposed methodology, the simulation results of different experiments including system parameters changes and set-point variation are provided.

Suggested Citation

  • Haghighatdar, F. & Ataei, M., 2009. "Adaptive set-point tracking of the Lorenz chaotic system using non-linear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1938-1945.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1938-1945
    DOI: 10.1016/j.chaos.2007.09.087
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    References listed on IDEAS

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    1. Pishkenari, H.N. & Shahrokhi, M. & Mahboobi, S.H., 2007. "Adaptive regulation and set-point tracking of the Lorenz attractor," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 832-846.
    2. Gambino, Gaetana & Lombardo, Maria Carmela & Sammartino, Marco, 2006. "Global linear feedback control for the generalized Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 829-837.
    3. Yau, Her-Terng & Chen, Chieh-Li, 2007. "Chaos control of Lorenz systems using adaptive controller with input saturation," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1567-1574.
    4. Wu, Xiaoqun & Lu, Jun-an & Tse, Chi K. & Wang, Jinjun & Liu, Jie, 2007. "Impulsive control and synchronization of the Lorenz systems family," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 631-638.
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    Cited by:

    1. Balootaki, Mohammad Ahmadi & Rahmani, Hossein & Moeinkhah, Hossein & Mohammadzadeh, Ardashir, 2020. "On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).

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