The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach
In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated...
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MDPI AG
2021-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/8/1409 |
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| author | Jiawen Li Yi Zhang Zhenghong Jin |
| author_facet | Jiawen Li Yi Zhang Zhenghong Jin |
| author_sort | Jiawen Li |
| collection | DOAJ |
| description | In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM. |
| first_indexed | 2024-03-10T08:20:26Z |
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| language | English |
| last_indexed | 2024-03-10T08:20:26Z |
| publishDate | 2021-08-01 |
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| series | Symmetry |
| spelling | doaj.art-5ce5f8f217f34613836fb7db7db0a1022023-11-22T10:01:00ZengMDPI AGSymmetry2073-89942021-08-01138140910.3390/sym13081409The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model ApproachJiawen Li0Yi Zhang1Zhenghong Jin2School of Science, Shenyang University of Technology, Shenyang 110870, ChinaSchool of Science, Shenyang University of Technology, Shenyang 110870, ChinaState Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, ChinaIn this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM.https://www.mdpi.com/2073-8994/13/8/1409nonlinear singular systemssingular polynomial fuzzy modelsliding mode controlapproximationimpulse |
| spellingShingle | Jiawen Li Yi Zhang Zhenghong Jin The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach Symmetry nonlinear singular systems singular polynomial fuzzy model sliding mode control approximation impulse |
| title | The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach |
| title_full | The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach |
| title_fullStr | The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach |
| title_full_unstemmed | The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach |
| title_short | The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach |
| title_sort | approximation of the nonlinear singular system with impulses and sliding mode control via a singular polynomial fuzzy model approach |
| topic | nonlinear singular systems singular polynomial fuzzy model sliding mode control approximation impulse |
| url | https://www.mdpi.com/2073-8994/13/8/1409 |
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