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Novel command-filtered Nussbaum design for continuous-time nonlinear dynamical systems with multiple unknown high-frequency gains

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Abstract

Command filters (CFs) have been successfully developed to reduce computational complexity and eliminate the effect of filtering errors on control performance through a compensating mechanism. However, to deal with multiple unknown high-frequency gains, the CF design remains an open problem due to the gap between the compensating mechanism design and unknown high-frequency gains. This paper bridges this gap by developing two additional adaptive laws that can contribute to the compensating mechanism design in novel CFs while considering the effect of unknown high-frequency gains. In the novel Nussbaum design, the influences of filtering errors are taken into account by introducing compensating signals. In contrast to existing filter-based Nussbaum methods, the compensating signals developed in this paper can handle multiple unknown high-frequency gains on the basis of the additional adaptive laws. The effect of filtering errors on the tracking performance is analyzed within the Lyapunov stability framework, and it is shown that the boundedness of all signals in the closed-loop system with the presented design can be guaranteed. Simulation results validate the efficacy of the proposed command-filtered Nussbaum design scheme.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

This work was supported in part by the Natural Science Foundation of Beijing Municipality under Grant No. J210005, in part by the National Natural Science Foundation of China under Grant 61903028, and in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) (No. NRF-2020R1A2C1005449).

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Authors and Affiliations

  1. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

    Yongliang Yang & Liqiang Tang

  2. State Key Laboratory of Internet of Things and Smart City, Faculty of Science and Technology, University of Macau, Taipa, 999078, Macau, China

    Wencheng Zou

  3. School of Electrical Engineering, Korea University, Seoul, 136-701, Korea

    Choon Ki Ahn

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  1. Yongliang Yang
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  2. Liqiang Tang
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Correspondence to Choon Ki Ahn.

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Yang, Y., Tang, L., Zou, W. et al. Novel command-filtered Nussbaum design for continuous-time nonlinear dynamical systems with multiple unknown high-frequency gains. Nonlinear Dyn 111, 4313–4323 (2023). https://doi.org/10.1007/s11071-022-08112-z

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  • DOI: https://doi.org/10.1007/s11071-022-08112-z

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