A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints
We consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization method used in conjunction with a time scaling transform, the constrained optimal control problem is appro...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/752854 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554364595601408 |
|---|---|
| author | Xiangyu Gao Xian Zhang Yantao Wang |
| author_facet | Xiangyu Gao Xian Zhang Yantao Wang |
| author_sort | Xiangyu Gao |
| collection | DOAJ |
| description | We consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization method used in conjunction with a time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and the state. On this basis, a simple exact penalty function method is used to transform the constrained optimal parameter selection problem into a sequence of approximate unconstrained optimal control problems. It is shown that, if the penalty parameter is sufficiently large, the locally optimal solutions of these approximate unconstrained optimal control problems converge to the solution of the original optimal control problem. Finally, numerical simulations on two examples demonstrate the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-76835a402cc24a8dbe09b365d9e42f09 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-76835a402cc24a8dbe09b365d9e42f092025-02-03T05:51:39ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/752854752854A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality ConstraintsXiangyu Gao0Xian Zhang1Yantao Wang2School of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaWe consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization method used in conjunction with a time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and the state. On this basis, a simple exact penalty function method is used to transform the constrained optimal parameter selection problem into a sequence of approximate unconstrained optimal control problems. It is shown that, if the penalty parameter is sufficiently large, the locally optimal solutions of these approximate unconstrained optimal control problems converge to the solution of the original optimal control problem. Finally, numerical simulations on two examples demonstrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2014/752854 |
| spellingShingle | Xiangyu Gao Xian Zhang Yantao Wang A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints Abstract and Applied Analysis |
| title | A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints |
| title_full | A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints |
| title_fullStr | A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints |
| title_full_unstemmed | A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints |
| title_short | A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints |
| title_sort | simple exact penalty function method for optimal control problem with continuous inequality constraints |
| url | http://dx.doi.org/10.1155/2014/752854 |
| work_keys_str_mv | AT xiangyugao asimpleexactpenaltyfunctionmethodforoptimalcontrolproblemwithcontinuousinequalityconstraints AT xianzhang asimpleexactpenaltyfunctionmethodforoptimalcontrolproblemwithcontinuousinequalityconstraints AT yantaowang asimpleexactpenaltyfunctionmethodforoptimalcontrolproblemwithcontinuousinequalityconstraints AT xiangyugao simpleexactpenaltyfunctionmethodforoptimalcontrolproblemwithcontinuousinequalityconstraints AT xianzhang simpleexactpenaltyfunctionmethodforoptimalcontrolproblemwithcontinuousinequalityconstraints AT yantaowang simpleexactpenaltyfunctionmethodforoptimalcontrolproblemwithcontinuousinequalityconstraints |