An optimal control problem for the systems with integral boundary conditions
In this paper, we consider an optimal control problem with a «pure», integral boundary condition. The Green’s function is constructed. Using contracting Banach mappings, a sufficient condition for the existence and uniqueness of a solution to one class of integral boundary value problems fo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2023-03-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2023-109-1/10.pdf |
| _version_ | 1797843580483534848 |
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| author | M.J. Mardanov Y.A. Sharifov |
| author_facet | M.J. Mardanov Y.A. Sharifov |
| author_sort | M.J. Mardanov |
| collection | DOAJ |
| description | In this paper, we consider an optimal control problem with a «pure», integral boundary condition. The Green’s function is constructed. Using contracting Banach mappings, a sufficient condition for the existence and uniqueness of a solution to one class of integral boundary value problems for fixed admissible controls is established. Using the functional increment method, the Pontryagin‘s maximum principle is proved. The first and second variations of the functional are calculated. Further, various necessary conditions for optimality of the second order are obtained by using variations of controls. |
| first_indexed | 2024-04-09T17:07:43Z |
| format | Article |
| id | doaj.art-7af255c318544845a853ca73ae665170 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-04-09T17:07:43Z |
| publishDate | 2023-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-7af255c318544845a853ca73ae6651702023-04-20T10:42:14ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-03-01109111012310.31489/2023M1/110-123An optimal control problem for the systems with integral boundary conditionsM.J. MardanovY.A. Sharifov In this paper, we consider an optimal control problem with a «pure», integral boundary condition. The Green’s function is constructed. Using contracting Banach mappings, a sufficient condition for the existence and uniqueness of a solution to one class of integral boundary value problems for fixed admissible controls is established. Using the functional increment method, the Pontryagin‘s maximum principle is proved. The first and second variations of the functional are calculated. Further, various necessary conditions for optimality of the second order are obtained by using variations of controls.https://mathematics-vestnik.ksu.kz/apart/2023-109-1/10.pdf |
| spellingShingle | M.J. Mardanov Y.A. Sharifov An optimal control problem for the systems with integral boundary conditions Қарағанды университетінің хабаршысы. Математика сериясы |
| title | An optimal control problem for the systems with integral boundary conditions |
| title_full | An optimal control problem for the systems with integral boundary conditions |
| title_fullStr | An optimal control problem for the systems with integral boundary conditions |
| title_full_unstemmed | An optimal control problem for the systems with integral boundary conditions |
| title_short | An optimal control problem for the systems with integral boundary conditions |
| title_sort | optimal control problem for the systems with integral boundary conditions |
| url | https://mathematics-vestnik.ksu.kz/apart/2023-109-1/10.pdf |
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