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ℒ1 adaptive controller design for a class of fractional order uncertain systems

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  • Boulham, Ihab Abderraouf
  • Boubakir, Ahsene
  • Labiod, Salim

Abstract

ℒ1 adaptive control method is a new and effective technique to perform a robust tracking response with fast adaptation, its applications were generalized for both integer order affine and non-affine nonlinear systems. However, ℒ1 adaptive control scheme has not been yet investigated to control fractional order systems. In this work, an ℒ1 adaptive controller is designed based on a fractional order sliding surface to control a class of fractional order systems with matched uncertainties and external disturbances. The developed controller is able to achieve closed-loop stability with uniform performance bounds for system signals. Such that, increasing the adaptation gain can dramatically enhance the performances for both transient and steady state responses. Finally, the validity and the effectiveness of the controller is tested using a numerical simulation.

Suggested Citation

  • Boulham, Ihab Abderraouf & Boubakir, Ahsene & Labiod, Salim, 2022. "ℒ1 adaptive controller design for a class of fractional order uncertain systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 232-249.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:232-249
    DOI: 10.1016/j.matcom.2021.10.011
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    References listed on IDEAS

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    1. Labbadi, Moussa & Moussaoui, Hassan El, 2021. "An improved adaptive fractional-order fast integral terminal sliding mode control for distributed quadrotor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 120-134.
    2. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
    3. Zhu, Zhen & Lu, Jun-Guo, 2021. "Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach," Applied Mathematics and Computation, Elsevier, vol. 401(C).
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    Cited by:

    1. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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