Optimal control of Goursat–Darboux-type polyhedral differential inclusions
UDC 517.96, 517.97 We study the problem of optimal control of the Goursat–Darboux-type differential inclusions (DFIs) given by polyhedral set-valued mappings and, for this purpose, pose an auxiliary problem with discrete Goursat–Darboux inclusion. By using the Farkas theorem, we compute locally adjo...
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| Date: | 2026 |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9377 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860956089560858624 |
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| author | Mahmudov, Elimhan N. Mahmudov, Elimhan N. |
| author_facet | Mahmudov, Elimhan N. Mahmudov, Elimhan N. |
| author_sort | Mahmudov, Elimhan N. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-28T20:30:15Z |
| description | UDC 517.96, 517.97
We study the problem of optimal control of the Goursat–Darboux-type differential inclusions (DFIs) given by polyhedral set-valued mappings and, for this purpose, pose an auxiliary problem with discrete Goursat–Darboux inclusion. By using the Farkas theorem, we compute locally adjoint mappings (LAMs) and establish necessary and sufficient optimality conditions for the polyhedral discrete Goursat–Darboux inclusions. Further, by the discretization method, for the Goursat–Darboux-type polyhedral DFI, we formulate (by using solely the specific features of its polyhedral property), first for a discrete-approximate problem and then, for a continuous problem, necessary and sufficient optimality conditions in the form of Euler–Lagrange-type polyhedral inclusions. |
| doi_str_mv | 10.3842/umzh.v78i3-4.9377 |
| first_indexed | 2026-03-29T01:00:26Z |
| format | Article |
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| id | umjimathkievua-article-9377 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-29T01:00:26Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-93772026-03-28T20:30:15Z Optimal control of Goursat–Darboux-type polyhedral differential inclusions Optimal control of Goursat–Darboux-type polyhedral differential inclusions Mahmudov, Elimhan N. Mahmudov, Elimhan N. Approximate discrete Goursat-Darboux differential inclusions Euler-Lagrange polyhedral necessary and sufficient 39A14 34A60 39A70 35L20 49M25 UDC 517.96, 517.97 We study the problem of optimal control of the Goursat–Darboux-type differential inclusions (DFIs) given by polyhedral set-valued mappings and, for this purpose, pose an auxiliary problem with discrete Goursat–Darboux inclusion. By using the Farkas theorem, we compute locally adjoint mappings (LAMs) and establish necessary and sufficient optimality conditions for the polyhedral discrete Goursat–Darboux inclusions. Further, by the discretization method, for the Goursat–Darboux-type polyhedral DFI, we formulate (by using solely the specific features of its polyhedral property), first for a discrete-approximate problem and then, for a continuous problem, necessary and sufficient optimality conditions in the form of Euler–Lagrange-type polyhedral inclusions. УДК 517.96, 517.97 Оптимальне керування поліедральними диференціальними включеннями типу Гурса–Дарбу Статтю присвячено оптимальному керуванню диференціальними включеннями типу Гурса–Дарбу, заданими поліедральними багатозначними відображеннями; для цього було поставлено допомiжну задачу з дискретним включенням Гурса–Дарбу. Використовуючи теорему Фаркаша, обчислено локально спряжені відображення та доведено необхідні та достатні умови оптимальності для поліедральних дискретних включень Гурса–Дарбу. Далі, застосовуючи метод дискретизації поліедрального диференціального включення типу Гурса–Дарбу, спочатку для дискретно-апроксимаційної задачі, а потім і для неперервної задачі з використанням лише специфіки її поліедральної властивості сформульовано необхідні та достатні умови оптимальності у формі поліедральних включень типу Ейлера–Лагранжа. Institute of Mathematics, NAS of Ukraine 2026-03-28 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9377 10.3842/umzh.v78i3-4.9377 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 3-4 (2026); 209–210 Український математичний журнал; Том 78 № 3-4 (2026); 209–210 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9377/10635 Copyright (c) 2026 Elimhan N. Mahmudov |
| spellingShingle | Mahmudov, Elimhan N. Mahmudov, Elimhan N. Optimal control of Goursat–Darboux-type polyhedral differential inclusions |
| title | Optimal control of Goursat–Darboux-type polyhedral differential inclusions |
| title_alt | Optimal control of Goursat–Darboux-type polyhedral differential inclusions |
| title_full | Optimal control of Goursat–Darboux-type polyhedral differential inclusions |
| title_fullStr | Optimal control of Goursat–Darboux-type polyhedral differential inclusions |
| title_full_unstemmed | Optimal control of Goursat–Darboux-type polyhedral differential inclusions |
| title_short | Optimal control of Goursat–Darboux-type polyhedral differential inclusions |
| title_sort | optimal control of goursat–darboux-type polyhedral differential inclusions |
| topic_facet | Approximate discrete Goursat-Darboux differential inclusions Euler-Lagrange polyhedral necessary and sufficient 39A14 34A60 39A70 35L20 49M25 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9377 |
| work_keys_str_mv | AT mahmudovelimhann optimalcontrolofgoursatdarbouxtypepolyhedraldifferentialinclusions AT mahmudovelimhann optimalcontrolofgoursatdarbouxtypepolyhedraldifferentialinclusions |