Optimal discrete-valued control computation
In this paper, we consider an optimal control problem in which the control takes values from a discrete set and the state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal control prob...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Springer
2013
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/26225 |
| _version_ | 1848751925402533888 |
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| author | Yu, Changjun Li, B. Loxton, Ryan Teo, Kok Lay |
| author_facet | Yu, Changjun Li, B. Loxton, Ryan Teo, Kok Lay |
| author_sort | Yu, Changjun |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider an optimal control problem in which the control takes values from a discrete set and the state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal control problem into an equivalent problem subject to additional linear and quadratic constraints. The feasible region defined by these additional constraints is disconnected, and thus standard optimization methods struggle to handle these constraints. We introduce a novel exact penalty function to penalize constraint violations, and then append this penalty function to the objective. This leads to an approximate optimal control problem that can be solved using standard software packages such as MISER. Convergence results show that when the penalty parameter is sufficiently large, any local solution of the approximate problem is also a local solution of the original problem. We conclude the paper with some numerical results for two difficult train control problems. |
| first_indexed | 2025-11-14T08:00:28Z |
| format | Journal Article |
| id | curtin-20.500.11937-26225 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:00:28Z |
| publishDate | 2013 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-262252019-02-19T05:35:35Z Optimal discrete-valued control computation Yu, Changjun Li, B. Loxton, Ryan Teo, Kok Lay Exact penalty function Time scaling transformation Optimal discrete-valued control In this paper, we consider an optimal control problem in which the control takes values from a discrete set and the state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal control problem into an equivalent problem subject to additional linear and quadratic constraints. The feasible region defined by these additional constraints is disconnected, and thus standard optimization methods struggle to handle these constraints. We introduce a novel exact penalty function to penalize constraint violations, and then append this penalty function to the objective. This leads to an approximate optimal control problem that can be solved using standard software packages such as MISER. Convergence results show that when the penalty parameter is sufficiently large, any local solution of the approximate problem is also a local solution of the original problem. We conclude the paper with some numerical results for two difficult train control problems. 2013 Journal Article http://hdl.handle.net/20.500.11937/26225 10.1007/s10898-012-9858-7 Springer fulltext |
| spellingShingle | Exact penalty function Time scaling transformation Optimal discrete-valued control Yu, Changjun Li, B. Loxton, Ryan Teo, Kok Lay Optimal discrete-valued control computation |
| title | Optimal discrete-valued control computation |
| title_full | Optimal discrete-valued control computation |
| title_fullStr | Optimal discrete-valued control computation |
| title_full_unstemmed | Optimal discrete-valued control computation |
| title_short | Optimal discrete-valued control computation |
| title_sort | optimal discrete-valued control computation |
| topic | Exact penalty function Time scaling transformation Optimal discrete-valued control |
| url | http://hdl.handle.net/20.500.11937/26225 |