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A New Nussbaum-Type Function and its Application in the Control of Uncertain Strict-Feedback Systems

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Abstract

In this study, an adaptive fuzzy output tracking control scheme is proposed for uncertain strict-feedback systems with unknown control directions. Nussbaum-type functions are designed, with which the effects of multiple unknown control directions can be handled. Compared with the existing Nussbaum-type functions dealing with the same problem, the proposed Nussbaum-type functions have smaller amplitudes that are more conducive to the design of the controller. Fuzzy functions are used to estimate the unknown terms by combining adaptive laws with backstepping procedure. Adaptive fuzzy controller is constructed to guarantee that the output tracking error system is asymptotically stable and all states in the closed-loop system are bounded. Finally, numerical simulation studies are presented to illustrate the effectiveness of the proposed criteria.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (61967001), the Natural Science Foundation of Anhui Province of China (1808085MF181), the Anhui Province Excellent Talents Project under Grant gxyq (2018065) and the Natural Science Foundation for the Higher Education Institutions of Anhui Province of China (KJ2016A666, KJ2019A0696).

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Authors and Affiliations

  1. Department of Applied Mathematics, Huainan Normal University, Huainan, 232038, China

    Ning Li, Wei Xiang & Jin Xu

  2. School of Science, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, 530006, China

    Heng Liu

  3. School of Management, Hefei University of Technology, Hefei, 230002, China

    Yaguang Li

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  1. Ning Li
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  2. Heng Liu
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  3. Yaguang Li
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  4. Wei Xiang
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  5. Jin Xu
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Correspondence to Yaguang Li.

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Li, N., Liu, H., Li, Y. et al. A New Nussbaum-Type Function and its Application in the Control of Uncertain Strict-Feedback Systems. Int. J. Fuzzy Syst. 22, 2284–2299 (2020). https://doi.org/10.1007/s40815-020-00909-7

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  • DOI: https://doi.org/10.1007/s40815-020-00909-7

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