Switching time optimization for nonlinear switched systems: Direct optimization and the time-scaling transformation
Given a switched system with multiple operating modes, a fundamental problem is to determine the optimal times at which the system should switch from one mode to another. This paper investigates two computational approaches for solving this problem-the direct optimization approach and the time-scali...
| Main Authors: | , , |
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| Format: | Journal Article |
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Yokohama Publishers
2014
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| Online Access: | http://www.ybook.co.jp/online2/pjov10.html http://hdl.handle.net/20.500.11937/19892 |
| _version_ | 1848750158394687488 |
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| author | Loxton, Ryan Lin, Qun Teo, Kok Lay |
| author_facet | Loxton, Ryan Lin, Qun Teo, Kok Lay |
| author_sort | Loxton, Ryan |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Given a switched system with multiple operating modes, a fundamental problem is to determine the optimal times at which the system should switch from one mode to another. This paper investigates two computational approaches for solving this problem-the direct optimization approach and the time-scaling approach. The direct optimization approach involves optimizing the mode switching times directly using gradient-based optimization methods such as sequential quadratic programming. The time-scaling approach involves transforming the switched system with variable switching times into an equivalent switched system with fixed switching times, where the decision parameters in the new switched system represent the mode durations in the original system. The optimal values for these new decision parameters-which can be obtained using conventional dynamic optimization techniques-then yield the optimal switching times for the original system. It is widely claimed in the literature that the time-scaling approach is superior to the direct optimization approach. However, the reasons given for its superiority are often vague, and sometimes incorrect. In this paper, we rigorously explicate the major advantages of the time-scaling transformation. We also compare the time-scaling and direct optimization approaches by solving a trajectory optimization problem involving the classical Dubins vehicle model. |
| first_indexed | 2025-11-14T07:32:23Z |
| format | Journal Article |
| id | curtin-20.500.11937-19892 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:32:23Z |
| publishDate | 2014 |
| publisher | Yokohama Publishers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-198922017-01-30T12:16:19Z Switching time optimization for nonlinear switched systems: Direct optimization and the time-scaling transformation Loxton, Ryan Lin, Qun Teo, Kok Lay switching times time-scaling transformation switched system gradient-based optimization Given a switched system with multiple operating modes, a fundamental problem is to determine the optimal times at which the system should switch from one mode to another. This paper investigates two computational approaches for solving this problem-the direct optimization approach and the time-scaling approach. The direct optimization approach involves optimizing the mode switching times directly using gradient-based optimization methods such as sequential quadratic programming. The time-scaling approach involves transforming the switched system with variable switching times into an equivalent switched system with fixed switching times, where the decision parameters in the new switched system represent the mode durations in the original system. The optimal values for these new decision parameters-which can be obtained using conventional dynamic optimization techniques-then yield the optimal switching times for the original system. It is widely claimed in the literature that the time-scaling approach is superior to the direct optimization approach. However, the reasons given for its superiority are often vague, and sometimes incorrect. In this paper, we rigorously explicate the major advantages of the time-scaling transformation. We also compare the time-scaling and direct optimization approaches by solving a trajectory optimization problem involving the classical Dubins vehicle model. 2014 Journal Article http://hdl.handle.net/20.500.11937/19892 http://www.ybook.co.jp/online2/pjov10.html Yokohama Publishers restricted |
| spellingShingle | switching times time-scaling transformation switched system gradient-based optimization Loxton, Ryan Lin, Qun Teo, Kok Lay Switching time optimization for nonlinear switched systems: Direct optimization and the time-scaling transformation |
| title | Switching time optimization for nonlinear switched systems: Direct optimization and the time-scaling transformation |
| title_full | Switching time optimization for nonlinear switched systems: Direct optimization and the time-scaling transformation |
| title_fullStr | Switching time optimization for nonlinear switched systems: Direct optimization and the time-scaling transformation |
| title_full_unstemmed | Switching time optimization for nonlinear switched systems: Direct optimization and the time-scaling transformation |
| title_short | Switching time optimization for nonlinear switched systems: Direct optimization and the time-scaling transformation |
| title_sort | switching time optimization for nonlinear switched systems: direct optimization and the time-scaling transformation |
| topic | switching times time-scaling transformation switched system gradient-based optimization |
| url | http://www.ybook.co.jp/online2/pjov10.html http://hdl.handle.net/20.500.11937/19892 |