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Adaptive robust control of fractional-order systems with matched and mismatched disturbances

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  • Muñoz-Vázquez, Aldo Jonathan
  • Ortiz-Moctezuma, Manuel Benjamín
  • Sánchez-Orta, Anand
  • Parra-Vega, Vicente

Abstract

This paper proposes an adaptive control method for the robust stabilization of a general class of fractional-order systems, which are subject to matched and mismatched disturbances. The control design is based on a nominal linear-time-invariant system, and the deviation from such a model is considered as the disturbance, which is decoupled as the sum of a matched and a mismatched disturbance. The controller is proposed as the combination of an adaptive robust controller that compensates for the matched disturbance, and a nominal controller that is based on a linear matrix inequality, in order to enforce the Mittag-Leffler stability of the pseudo-state, even in the presence of the mismatched disturbance. Numerical simulations are conducted to show the reliability of the proposed scheme.

Suggested Citation

  • Muñoz-Vázquez, Aldo Jonathan & Ortiz-Moctezuma, Manuel Benjamín & Sánchez-Orta, Anand & Parra-Vega, Vicente, 2019. "Adaptive robust control of fractional-order systems with matched and mismatched disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 85-96.
    • Handle: RePEc:eee:matcom:v:162:y:2019:i:c:p:85-96
    DOI: 10.1016/j.matcom.2019.01.008
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    References listed on IDEAS

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    1. David, S.A. & Machado, J.A.T. & Quintino, D.D. & Balthazar, J.M., 2016. "Partial chaos suppression in a fractional order macroeconomic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 55-68.
    2. Yiheng Wei & Zhenyuan Sun & Yangsheng Hu & Yong Wang, 2016. "On fractional order composite model reference adaptive control," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(11), pages 2521-2531, August.
    3. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2009. "A note on the stability of fractional order systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1566-1576.
    4. Huang, Li-Lian & Zhang, Juan & Shi, Shuai-Shuai, 2015. "Circuit simulation on control and synchronization of fractional order switching chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 113(C), pages 28-39.
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    Cited by:

    1. Yaghoubi, Zahra, 2020. "Robust cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding mode controller," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 15-32.
    2. Allan G. Soriano-Sánchez & Martín A. Rodríguez-Licea & Francisco J. Pérez-Pinal & José A. Vázquez-López, 2020. "Fractional-Order Approximation and Synthesis of a PID Controller for a Buck Converter," Energies, MDPI, vol. 13(3), pages 1-17, February.

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