Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties
This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs....
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/4/4/50 |
| _version_ | 1827703730326208512 |
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| author | Xuefeng Zhang Wenkai Huang |
| author_facet | Xuefeng Zhang Wenkai Huang |
| author_sort | Xuefeng Zhang |
| collection | DOAJ |
| description | This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs. Firstly, by expanding the dimension of the SFOS, a novel sliding surface was constructed. A necessary and sufficient condition was given to ensure the admissibility of the SFOS while the system state moves on the sliding surface. The obtained results are linear matrix inequalities (LMIs), which are more general than the existing research. Then, the adaptive control law based on the RBF neural network was organized to guarantee that the SFOS reaches the sliding surface in a finite time. Finally, a simulation example is proposed to verify the validity of the designed procedures. |
| first_indexed | 2024-03-10T15:25:01Z |
| format | Article |
| id | doaj.art-d44c69a1d2404fae971bd8e556e3feba |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T15:25:01Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d44c69a1d2404fae971bd8e556e3feba2023-11-20T18:12:29ZengMDPI AGFractal and Fractional2504-31102020-10-01445010.3390/fractalfract4040050Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched UncertaintiesXuefeng Zhang0Wenkai Huang1College of Sciences, Northeastern University, Shenyang 110819, ChinaCollege of Sciences, Northeastern University, Shenyang 110819, ChinaThis paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs. Firstly, by expanding the dimension of the SFOS, a novel sliding surface was constructed. A necessary and sufficient condition was given to ensure the admissibility of the SFOS while the system state moves on the sliding surface. The obtained results are linear matrix inequalities (LMIs), which are more general than the existing research. Then, the adaptive control law based on the RBF neural network was organized to guarantee that the SFOS reaches the sliding surface in a finite time. Finally, a simulation example is proposed to verify the validity of the designed procedures.https://www.mdpi.com/2504-3110/4/4/50singular fractional order systemslinear matrix inequalityadaptive RBF neural networksliding mode control |
| spellingShingle | Xuefeng Zhang Wenkai Huang Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties Fractal and Fractional singular fractional order systems linear matrix inequality adaptive RBF neural network sliding mode control |
| title | Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties |
| title_full | Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties |
| title_fullStr | Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties |
| title_full_unstemmed | Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties |
| title_short | Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties |
| title_sort | adaptive neural network sliding mode control for nonlinear singular fractional order systems with mismatched uncertainties |
| topic | singular fractional order systems linear matrix inequality adaptive RBF neural network sliding mode control |
| url | https://www.mdpi.com/2504-3110/4/4/50 |
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