Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems
Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical tech...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/240352 |
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| _version_ | 1832563634695307264 |
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| author | Waleeda Swaidan Amran Hussin |
| author_facet | Waleeda Swaidan Amran Hussin |
| author_sort | Waleeda Swaidan |
| collection | DOAJ |
| description | Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution. |
| format | Article |
| id | doaj-art-58d48cfe880e435ea5248f8e843513c9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-58d48cfe880e435ea5248f8e843513c92025-02-03T01:12:59ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/240352240352Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control ProblemsWaleeda Swaidan0Amran Hussin1Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, MalaysiaInstitute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, MalaysiaMost of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution.http://dx.doi.org/10.1155/2013/240352 |
| spellingShingle | Waleeda Swaidan Amran Hussin Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems Abstract and Applied Analysis |
| title | Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems |
| title_full | Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems |
| title_fullStr | Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems |
| title_full_unstemmed | Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems |
| title_short | Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems |
| title_sort | feedback control method using haar wavelet operational matrices for solving optimal control problems |
| url | http://dx.doi.org/10.1155/2013/240352 |
| work_keys_str_mv | AT waleedaswaidan feedbackcontrolmethodusinghaarwaveletoperationalmatricesforsolvingoptimalcontrolproblems AT amranhussin feedbackcontrolmethodusinghaarwaveletoperationalmatricesforsolvingoptimalcontrolproblems |