An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem
In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous state and control inequality constraints. By using the control parametrization technique and a time scaling transformation, the constrained optimal control problem is approxim...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Springer Netherlands
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/24732 |
| _version_ | 1848751510963355648 |
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| author | Li, Bin Yu, Changjun Teo, Kok Lay Duan, G. |
| author_facet | Li, Bin Yu, Changjun Teo, Kok Lay Duan, G. |
| author_sort | Li, Bin |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous state and control inequality constraints. By using the control parametrization technique and a time scaling transformation, the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality terminal state constraints and continuous state inequality constraints. Each of these constrained optimal parameter selection problems can be regarded as an optimization problem subject to equality constraints and continuous inequality constraints. On this basis, an exact penalty function method is used to devise a computational method to solve these optimization problems with equality constraints and continuous inequality constraints. The main idea is to augment the exact penalty function constructed from the equality constraints and continuous inequality constraints to the objective function, forming a new one. This gives rise to a sequence of unconstrained optimization problems. It is shown that, for sufficiently large penalty parameter value, any local minimizer of the unconstrained optimization problem is a local minimizer of the optimization problem with equality constraints and continuous inequality constraints. The convergent properties of the optimal parameter selection problems with equality constraints and continuous inequality constraints to the original optimal control problem are also discussed. For illustration, three examples are solved showing the effectiveness and applicability of the approach proposed. |
| first_indexed | 2025-11-14T07:53:53Z |
| format | Journal Article |
| id | curtin-20.500.11937-24732 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:53:53Z |
| publishDate | 2011 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-247322017-09-13T15:51:04Z An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem Li, Bin Yu, Changjun Teo, Kok Lay Duan, G. In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous state and control inequality constraints. By using the control parametrization technique and a time scaling transformation, the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality terminal state constraints and continuous state inequality constraints. Each of these constrained optimal parameter selection problems can be regarded as an optimization problem subject to equality constraints and continuous inequality constraints. On this basis, an exact penalty function method is used to devise a computational method to solve these optimization problems with equality constraints and continuous inequality constraints. The main idea is to augment the exact penalty function constructed from the equality constraints and continuous inequality constraints to the objective function, forming a new one. This gives rise to a sequence of unconstrained optimization problems. It is shown that, for sufficiently large penalty parameter value, any local minimizer of the unconstrained optimization problem is a local minimizer of the optimization problem with equality constraints and continuous inequality constraints. The convergent properties of the optimal parameter selection problems with equality constraints and continuous inequality constraints to the original optimal control problem are also discussed. For illustration, three examples are solved showing the effectiveness and applicability of the approach proposed. 2011 Journal Article http://hdl.handle.net/20.500.11937/24732 10.1007/s10957-011-9904-5 Springer Netherlands restricted |
| spellingShingle | Li, Bin Yu, Changjun Teo, Kok Lay Duan, G. An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem |
| title | An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem |
| title_full | An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem |
| title_fullStr | An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem |
| title_full_unstemmed | An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem |
| title_short | An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem |
| title_sort | exact penalty function method for continuous inequality constrained optimal control problem |
| url | http://hdl.handle.net/20.500.11937/24732 |