Control parameterization for optimal control problems with continuous inequality constraints: New convergence results
Control parameterization is a powerful numerical technique for solving optimal control problems with general nonlinear constraints. The main idea of control parameterization is to discretize the control space by approximating the control by a piecewise-constant or piecewise-linear function, thereby...
| Main Authors: | , , , |
|---|---|
| Format: | Journal Article |
| Published: |
American Institute of Mathematical Sciences
2012
|
| Online Access: | http://hdl.handle.net/20.500.11937/23872 |
| _version_ | 1848751272600010752 |
|---|---|
| author | Loxton, Ryan Lin, Qun Rehbock, Volker Teo, Kok Lay |
| author_facet | Loxton, Ryan Lin, Qun Rehbock, Volker Teo, Kok Lay |
| author_sort | Loxton, Ryan |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Control parameterization is a powerful numerical technique for solving optimal control problems with general nonlinear constraints. The main idea of control parameterization is to discretize the control space by approximating the control by a piecewise-constant or piecewise-linear function, thereby yielding an approximate nonlinear programming problem. This approximate problem can then be solved using standard gradient-based optimization techniques. In this paper, we consider the control parameterization method for a class of optimal control problems in which the admissible controls are functions of bounded variation and the state and control are subject to continuous inequality constraints. We show that control parameterization generates a sequence of suboptimal controls whose costs converge to the true optimal cost. This result has previously only been proved for the case when the admissible controls are restricted to piecewise continuous functions. |
| first_indexed | 2025-11-14T07:50:06Z |
| format | Journal Article |
| id | curtin-20.500.11937-23872 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:50:06Z |
| publishDate | 2012 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-238722019-02-19T05:35:06Z Control parameterization for optimal control problems with continuous inequality constraints: New convergence results Loxton, Ryan Lin, Qun Rehbock, Volker Teo, Kok Lay Control parameterization is a powerful numerical technique for solving optimal control problems with general nonlinear constraints. The main idea of control parameterization is to discretize the control space by approximating the control by a piecewise-constant or piecewise-linear function, thereby yielding an approximate nonlinear programming problem. This approximate problem can then be solved using standard gradient-based optimization techniques. In this paper, we consider the control parameterization method for a class of optimal control problems in which the admissible controls are functions of bounded variation and the state and control are subject to continuous inequality constraints. We show that control parameterization generates a sequence of suboptimal controls whose costs converge to the true optimal cost. This result has previously only been proved for the case when the admissible controls are restricted to piecewise continuous functions. 2012 Journal Article http://hdl.handle.net/20.500.11937/23872 10.3934/naco.2012.2.571 American Institute of Mathematical Sciences fulltext |
| spellingShingle | Loxton, Ryan Lin, Qun Rehbock, Volker Teo, Kok Lay Control parameterization for optimal control problems with continuous inequality constraints: New convergence results |
| title | Control parameterization for optimal control problems with continuous inequality constraints: New convergence results |
| title_full | Control parameterization for optimal control problems with continuous inequality constraints: New convergence results |
| title_fullStr | Control parameterization for optimal control problems with continuous inequality constraints: New convergence results |
| title_full_unstemmed | Control parameterization for optimal control problems with continuous inequality constraints: New convergence results |
| title_short | Control parameterization for optimal control problems with continuous inequality constraints: New convergence results |
| title_sort | control parameterization for optimal control problems with continuous inequality constraints: new convergence results |
| url | http://hdl.handle.net/20.500.11937/23872 |