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\({L_\infty }\) Fault Estimation and Fault-Tolerant Control for Nonlinear Systems by T–S Fuzzy Model Method with Local Nonlinear Models

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Abstract

This paper investigates the problems of the observer-based fault estimation (FE) and fault-tolerant control (FTC) for nonlinear systems subjected to external disturbances by the T–S fuzzy model method with local nonlinear models. Firstly, an FE strategy is proposed based on the unknown input observer technology, where the local nonlinear terms can be decoupled from the FE error system for relaxing the design of observer. Then, by using the FE information, a fuzzy fault-tolerant controller is designed to guarantee the stability of the system. Additionally, in the design schemes of the FE observer and the fault-tolerant controller, the \({L_\infty }\) method is used to deal with the problems of FE and FTC for the system with persistent disturbance such that the robustness of the system against the persistent external disturbance can be increased. Compared with the traditional \({H_\infty }\) method which is only applicable for dealing with the energy bounded signals, the \({L_\infty }\) FTC strategy proposed in this paper can deal with the persistent disturbance such that the shortcomings of the traditional \({H_\infty }\) approach are overcome. Finally, the effectiveness of the proposed method is verified by simulation results.

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Acknowledgements

This work is supported in part by the National Natural Science Foundation of China (under Grant Nos. 51939001, 62003069, 61976033, U1813203, 61751202, 61773187); the Science and Technology Innovation Funds of Dalian (under Grant No. 2018J11CY022); the LiaoNing Revitalization Talents Program (under Grant Nos. XLYC1908018); the Natural Foundation Guidance Plan Project of Liaoning (2019-ZD-0151); the Fundamental Research Funds for the Central Universities (under Grant Nos. 3132020126, 3132019345); the Science and Technology Development Fund, Macau SAR (File no. SKL-IOTSC-2018-2020, 0018/2019/AKP); the Natural Science Foundation of Liaoning Province under Grant 20170540098.

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Authors and Affiliations

  1. Navigation College, Dalian Maritime University, Dalian, 116026, China

    Yang Wang, Tieshan Li, Ximing Yang, C. L. Philip Chen & Jun Ning

  2. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Tieshan Li & Yue Long

  3. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 611756, China

    Yue Wu

  4. Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau, 99999, China

    C. L. Philip Chen

  5. State Key Laboratory of Internet of Things for Smart City and Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Macau, SAR, China

    Zhixin Yang

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  1. Yang Wang
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Correspondence to Tieshan Li.

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Wang, Y., Li, T., Wu, Y. et al. \({L_\infty }\) Fault Estimation and Fault-Tolerant Control for Nonlinear Systems by T–S Fuzzy Model Method with Local Nonlinear Models. Int. J. Fuzzy Syst. 23, 1714–1727 (2021). https://doi.org/10.1007/s40815-021-01061-6

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