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Generalized adaptive gain sliding mode observer for uncertain nonlinear systems

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Abstract

This paper proposes a new generalized adaptive gain sliding mode observer (GAGSMO) for estimating the unavailable states of a class of multi-input multi-output uncertain nonlinear systems. To further improve the estimation performance of conventional sliding mode observer, the observer gains of GAGSMO are designed for the first time as the generalized bounded positive functions of the available output errors and the upper bounds of disturbance terms. Due to the features of the designed observer gains, the GAGSMO has stronger robustness than the conventional sliding mode observer in the presence of system uncertainties and nonlinearities. The finite-time error convergence of GAGSMO is proved by the Lyapunov stability theorem in conjunction with the introduced mapping functions. Then, by catching sight of the inherent feature of sliding motion, a recursive mechanism based only on available estimation information is formulated to update the designed observer gains online in the sliding mode stage. With the recursive mechanism, the chattering level of GAGSMO is minimized, and the estimation accuracy of GAGSMO is further improved. The effectiveness and excellent performance of the proposed GAGSMO are illustrated with two numerical examples.

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Acknowledgements

This study was supported by a grant from the Key Research and Development Program of Anhui Province (No. 202104a05020035) and the State Scholarship Fund of China Scholarship Council (No. 201806690018). The authors would like to thank the editor-in-chief, the associate editor, and the anonymous reviewers for their invaluable comments to improve this work.

Funding

Anhui Provincial Key Research and Development Plan, 202104a05020035, Huifang Kong.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, China

    Xiaoxue Zhang & Huifang Kong

  2. School of Software and Electrical Engineering, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC, 3122, Australia

    Zhihong Man

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  1. Xiaoxue Zhang
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All authors contributed to the conception and design. The first draft of the manuscript was written by XZ and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Xiaoxue Zhang.

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Zhang, X., Kong, H. & Man, Z. Generalized adaptive gain sliding mode observer for uncertain nonlinear systems. Nonlinear Dyn 111, 22237–22253 (2023). https://doi.org/10.1007/s11071-023-09000-w

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