LS-SVM approximate solution for affine nonlinear systems with partially unknown functions
By using the Least Squares Support Vector Machines (LS-SVMs), we develop a numerical approach to find an approximate solution for affine nonlinear systems with partially unknown functions. This approach can obtain continuous and differential approximate solutions of the nonlinear differential equati...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
American Institute of Mathematical Sciences
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/49945 |
| _version_ | 1848758356314947584 |
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| author | Zhang, G. Wang, S. Wang, Y. Liu, Wan-Quan |
| author_facet | Zhang, G. Wang, S. Wang, Y. Liu, Wan-Quan |
| author_sort | Zhang, G. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | By using the Least Squares Support Vector Machines (LS-SVMs), we develop a numerical approach to find an approximate solution for affine nonlinear systems with partially unknown functions. This approach can obtain continuous and differential approximate solutions of the nonlinear differential equations, and can also identify the unknown nonlinear part through a set of measured data points. Technically, we first map the known part of the affine nonlinear systems into high dimensional feature spaces and derive the form of approximate solution. Then the original problem is formulated as an approximation problem via kernel trick with LS-SVMs. Furthermore, the approximation of the known part can be expressed via some linear equations with coefficient matrices as coupling square matrices, and the unknown part can be identified by its relationship to the known part and the approximate solution of affine nonlinear systems. Finally, several examples for different systems are presented to illustrate the validity of the proposed approach. |
| first_indexed | 2025-11-14T09:42:41Z |
| format | Journal Article |
| id | curtin-20.500.11937-49945 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:42:41Z |
| publishDate | 2014 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-499452017-09-13T15:50:49Z LS-SVM approximate solution for affine nonlinear systems with partially unknown functions Zhang, G. Wang, S. Wang, Y. Liu, Wan-Quan By using the Least Squares Support Vector Machines (LS-SVMs), we develop a numerical approach to find an approximate solution for affine nonlinear systems with partially unknown functions. This approach can obtain continuous and differential approximate solutions of the nonlinear differential equations, and can also identify the unknown nonlinear part through a set of measured data points. Technically, we first map the known part of the affine nonlinear systems into high dimensional feature spaces and derive the form of approximate solution. Then the original problem is formulated as an approximation problem via kernel trick with LS-SVMs. Furthermore, the approximation of the known part can be expressed via some linear equations with coefficient matrices as coupling square matrices, and the unknown part can be identified by its relationship to the known part and the approximate solution of affine nonlinear systems. Finally, several examples for different systems are presented to illustrate the validity of the proposed approach. 2014 Journal Article http://hdl.handle.net/20.500.11937/49945 10.3934/jimo.2014.10.621 American Institute of Mathematical Sciences unknown |
| spellingShingle | Zhang, G. Wang, S. Wang, Y. Liu, Wan-Quan LS-SVM approximate solution for affine nonlinear systems with partially unknown functions |
| title | LS-SVM approximate solution for affine nonlinear systems with partially unknown functions |
| title_full | LS-SVM approximate solution for affine nonlinear systems with partially unknown functions |
| title_fullStr | LS-SVM approximate solution for affine nonlinear systems with partially unknown functions |
| title_full_unstemmed | LS-SVM approximate solution for affine nonlinear systems with partially unknown functions |
| title_short | LS-SVM approximate solution for affine nonlinear systems with partially unknown functions |
| title_sort | ls-svm approximate solution for affine nonlinear systems with partially unknown functions |
| url | http://hdl.handle.net/20.500.11937/49945 |