Numerical Solution of Fractional Optimal Control
This paper presents a numerical algorithm for solving a class of nonlinear optimal control problems subject to a system of fractional differential equations. We first propose a robust second-order numerical integration scheme for the system. The objective is approximated by the trapezoidal rule. We...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer New York LLC
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/72834 |
| _version_ | 1848762853843009536 |
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| author | Li, W. Wang, Song Rehbock, Volker |
| author_facet | Li, W. Wang, Song Rehbock, Volker |
| author_sort | Li, W. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper presents a numerical algorithm for solving a class of nonlinear optimal control problems subject to a system of fractional differential equations. We first propose a robust second-order numerical integration scheme for the system. The objective is approximated by the trapezoidal rule. We then apply a gradient-based optimization method to the discretized problem. Formulas for calculating the gradients are derived. Computational results demonstrate that our method is able to generate accurate numerical approximations for problems with multiple states and controls. It is also robust with respect to the fractional orders of derivatives. |
| first_indexed | 2025-11-14T10:54:10Z |
| format | Journal Article |
| id | curtin-20.500.11937-72834 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:54:10Z |
| publishDate | 2018 |
| publisher | Springer New York LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-728342019-03-06T06:46:57Z Numerical Solution of Fractional Optimal Control Li, W. Wang, Song Rehbock, Volker This paper presents a numerical algorithm for solving a class of nonlinear optimal control problems subject to a system of fractional differential equations. We first propose a robust second-order numerical integration scheme for the system. The objective is approximated by the trapezoidal rule. We then apply a gradient-based optimization method to the discretized problem. Formulas for calculating the gradients are derived. Computational results demonstrate that our method is able to generate accurate numerical approximations for problems with multiple states and controls. It is also robust with respect to the fractional orders of derivatives. 2018 Journal Article http://hdl.handle.net/20.500.11937/72834 10.1007/s10957-018-1418-y Springer New York LLC restricted |
| spellingShingle | Li, W. Wang, Song Rehbock, Volker Numerical Solution of Fractional Optimal Control |
| title | Numerical Solution of Fractional Optimal Control |
| title_full | Numerical Solution of Fractional Optimal Control |
| title_fullStr | Numerical Solution of Fractional Optimal Control |
| title_full_unstemmed | Numerical Solution of Fractional Optimal Control |
| title_short | Numerical Solution of Fractional Optimal Control |
| title_sort | numerical solution of fractional optimal control |
| url | http://hdl.handle.net/20.500.11937/72834 |