On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System
We use the initial condition on the state variable of a hyperbolic problem as control function and formulate a control problem whose solution implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and given targets. We prove the exi...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/156541 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559489157431296 |
|---|---|
| author | Yeşim Saraç Murat Subaşı |
| author_facet | Yeşim Saraç Murat Subaşı |
| author_sort | Yeşim Saraç |
| collection | DOAJ |
| description | We use the initial condition on the state variable of a hyperbolic problem as control function and formulate a control problem whose solution implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and given targets. We prove the existence and the uniqueness of the optimal solution and establish the optimality condition. An iterative algorithm is constructed to compute the required optimal control as limit of a suitable subsequence of controls. An iterative procedure is implemented and used to numerically solve some test problems. |
| format | Article |
| id | doaj-art-68b17077aed84c5aa3d2d7706671aa1a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-68b17077aed84c5aa3d2d7706671aa1a2025-02-03T01:29:57ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/156541156541On the Regularized Solutions of Optimal Control Problem in a Hyperbolic SystemYeşim Saraç0Murat Subaşı1Department of Mathematics, Faculty of Science, Atatürk University, 25240 Erzurum, TurkeyDepartment of Mathematics, Faculty of Science, Atatürk University, 25240 Erzurum, TurkeyWe use the initial condition on the state variable of a hyperbolic problem as control function and formulate a control problem whose solution implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and given targets. We prove the existence and the uniqueness of the optimal solution and establish the optimality condition. An iterative algorithm is constructed to compute the required optimal control as limit of a suitable subsequence of controls. An iterative procedure is implemented and used to numerically solve some test problems.http://dx.doi.org/10.1155/2012/156541 |
| spellingShingle | Yeşim Saraç Murat Subaşı On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System Abstract and Applied Analysis |
| title | On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System |
| title_full | On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System |
| title_fullStr | On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System |
| title_full_unstemmed | On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System |
| title_short | On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System |
| title_sort | on the regularized solutions of optimal control problem in a hyperbolic system |
| url | http://dx.doi.org/10.1155/2012/156541 |
| work_keys_str_mv | AT yesimsarac ontheregularizedsolutionsofoptimalcontrolprobleminahyperbolicsystem AT muratsubası ontheregularizedsolutionsofoptimalcontrolprobleminahyperbolicsystem |