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Fuzzy Command Filter Backstepping Control for Incommensurate Fractional-Order Systems via Composite Learning

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Abstract

This paper investigates the command filter backstepping control of uncertain fractional-order generalized strict-feedback nonlinear systems with input nonlinearities and functional uncertainties based on a composite learning method. The main motivations are that the simplification of backstepping control by providing the fractional-order command filter to avoid the calculation of the derivatives of virtual controller functions, and parameters convergence can be achieved without the strict persistency of excitation condition via fractional-order composite learning laws. In the controller design, both tracking errors and prediction errors are used to update adjusted parameters. Moreover, the analytic computation of derivatives of virtual inputs is not required. A set of lemmas is provided to analyze the affect of the fractional-order command filter, and the parameter convergence can be achieved without persistent excitation condition based on the composite learning technique. The control performance can be improved from the asymptotic stability to the M-L stability in closed-loop system. Finally, simulation result verifies the performance of the proposed method.

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Acknowledgements

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number (IFPRC-035-611-2020) and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

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Authors and Affiliations

  1. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia

    Fawaz E. Alsaadi, Madini O. Alassafi, Reem M. Alotaibi & Adil M. Ahmad

  2. School of Mathematics and Physics, Guangxi Minzu University, Nanning, 530006, China

    Xiulan Zhang

  3. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  4. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    Jinde Cao

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  1. Fawaz E. Alsaadi
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  2. Xiulan Zhang
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  3. Madini O. Alassafi
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  4. Reem M. Alotaibi
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  5. Adil M. Ahmad
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  6. Jinde Cao
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Correspondence to Xiulan Zhang.

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Alsaadi, F.E., Zhang, X., Alassafi, M.O. et al. Fuzzy Command Filter Backstepping Control for Incommensurate Fractional-Order Systems via Composite Learning. Int. J. Fuzzy Syst. 24, 3293–3307 (2022). https://doi.org/10.1007/s40815-022-01344-6

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  • DOI: https://doi.org/10.1007/s40815-022-01344-6

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