A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems
In this paper, we consider a class of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. We propose a new computational approach, which combines the control parameterization technique with a hybrid time-scaling strategy, for solving this class of optima...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
Springer New York LLC
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/19783 |
| _version_ | 1848750128326770688 |
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| author | Yu, Changjun Lin, Qun Loxton, R. Teo, Kok Lay Wang, G. |
| author_facet | Yu, Changjun Lin, Qun Loxton, R. Teo, Kok Lay Wang, G. |
| author_sort | Yu, Changjun |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a class of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. We propose a new computational approach, which combines the control parameterization technique with a hybrid time-scaling strategy, for solving this class of optimal control problems. The proposed approach involves approximating the control variables by piecewise constant functions, whose heights and switching times are decision variables to be optimized. Then, the resulting problem with varying switching times is transformed, via a new hybrid time-scaling strategy, into an equivalent problem with fixed switching times, which is much preferred for numerical computation. Our new time-scaling strategy is hybrid in the sense that it is related to two coupled time-delay systems—one defined on the original time scale, in which the switching times are variable, the other defined on the new time scale, in which the switching times are fixed. This is different from the conventional time-scaling transformation widely used in the literature, which is not applicable to systems with time-delays. To demonstrate the effectiveness of the proposed approach, we solve four numerical examples. The results show that the costs obtained by our new approach are lower, when compared with those obtained by existing optimal control methods. |
| first_indexed | 2025-11-14T07:31:54Z |
| format | Journal Article |
| id | curtin-20.500.11937-19783 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:31:54Z |
| publishDate | 2015 |
| publisher | Springer New York LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-197832018-10-08T01:25:17Z A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems Yu, Changjun Lin, Qun Loxton, R. Teo, Kok Lay Wang, G. In this paper, we consider a class of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. We propose a new computational approach, which combines the control parameterization technique with a hybrid time-scaling strategy, for solving this class of optimal control problems. The proposed approach involves approximating the control variables by piecewise constant functions, whose heights and switching times are decision variables to be optimized. Then, the resulting problem with varying switching times is transformed, via a new hybrid time-scaling strategy, into an equivalent problem with fixed switching times, which is much preferred for numerical computation. Our new time-scaling strategy is hybrid in the sense that it is related to two coupled time-delay systems—one defined on the original time scale, in which the switching times are variable, the other defined on the new time scale, in which the switching times are fixed. This is different from the conventional time-scaling transformation widely used in the literature, which is not applicable to systems with time-delays. To demonstrate the effectiveness of the proposed approach, we solve four numerical examples. The results show that the costs obtained by our new approach are lower, when compared with those obtained by existing optimal control methods. 2015 Journal Article http://hdl.handle.net/20.500.11937/19783 10.1007/s10957-015-0783-z Springer New York LLC fulltext |
| spellingShingle | Yu, Changjun Lin, Qun Loxton, R. Teo, Kok Lay Wang, G. A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems |
| title | A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems |
| title_full | A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems |
| title_fullStr | A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems |
| title_full_unstemmed | A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems |
| title_short | A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems |
| title_sort | hybrid time-scaling transformation for time-delay optimal control problems |
| url | http://hdl.handle.net/20.500.11937/19783 |