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Historical Data-Driven Composite Learning Adaptive Fuzzy Control of Fractional-Order Nonlinear Systems

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Abstract

Different from traditional adaptive fuzzy control, this paper introduces a composite learning adaptive backstepping fuzzy control method using historical data which mainly focuses on improving the approximation accuracy of fuzzy logic systems for functional uncertainties of fractional-order nonlinear systems. A command filter is employed to settle the “explosion of complexity” issue that resulted from differentiating virtual controllers repeatedly in each backstepping step, and a compensation signal is defined to reduce the impact of filtered errors on control performance. In addition, a modified prediction error is defined to construct a composite parameter adaptation law, where the compensated error dynamic system equation is integrated in a moving time interval such that all historical data are integrated into a regressor vector to calculate the prediction error. The method introduced can not only ensure the boundedness of all signals in the closed-loop system based on the fractional Lyapunov stability criterion, but also realize the precise approximation to functional uncertainties. Finally, two numerical simulation examples are presented to demonstrate the superior effect of the proposed method.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (12261009, 61967001), in part by the Innovation Project of Guangxi Graduate Education (YCSW2022251), and in part by the Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University (2019RSCXSHQN02).

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Authors and Affiliations

  1. College of Mathematics and Physics, Center for Applied Mathematics of Guangx, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, China

    Hongling Qiu, Heng Liu & Xiulan Zhang

  2. School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510006, China

    Hongling Qiu & Heng Liu

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  1. Hongling Qiu
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  2. Heng Liu
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  3. Xiulan Zhang
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Correspondence to Heng Liu.

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Qiu, H., Liu, H. & Zhang, X. Historical Data-Driven Composite Learning Adaptive Fuzzy Control of Fractional-Order Nonlinear Systems. Int. J. Fuzzy Syst. 25, 1156–1170 (2023). https://doi.org/10.1007/s40815-022-01430-9

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  • DOI: https://doi.org/10.1007/s40815-022-01430-9

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