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Fractional-Order Multivariable Adaptive Control Based on a Nonlinear Scalar Update Law

Author

Listed:
  • Fang Yan

    (School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Xiaorong Hou

    (School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Tingting Tian

    (School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

This paper proposes a new fractional-order model reference adaptive control (FOMRAC) framework for a fractional-order multivariable system with parameter uncertainty. The designed FOMRAC scheme depends on a fractional-order nonlinear scalar update law. Specifically, the scalar update law does not change as the input–output dimension changes. The main advantage of the proposed adaptive controller is that only one parameter online update is needed such that the computational burden in the existing FOMRAC can be relieved. Furthermore, we show that all signals in this adaptive scheme are bounded and the mean value of the squared norm of the error converges to zero. Two illustrative numerical examples are presented to demonstrate the efficiency of the proposed control scheme.

Suggested Citation

  • Fang Yan & Xiaorong Hou & Tingting Tian, 2022. "Fractional-Order Multivariable Adaptive Control Based on a Nonlinear Scalar Update Law," Mathematics, MDPI, vol. 10(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3385-:d:917924
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    References listed on IDEAS

    as
    1. Omar Kahouli & Assaad Jmal & Omar Naifar & Abdelhameed M. Nagy & Abdellatif Ben Makhlouf, 2022. "New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
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    Cited by:

    1. Yan, Fang & Hou, Xiaorong & Tian, Tingting & Chen, Xiaojie, 2023. "Nonlinear model reference adaptive control approach for governance of the commons in a feedback-evolving game," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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