Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem
We consider the approximate optimal control based on the principle of feedback relation (synthesis) for a parabolic boundary-value problem. We represent the feedback operator as Fourier series in the eigenfunctions of the Laplace operator, which does not enable us to use these results in practice. I...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4210 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510340582735872 |
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| author | Kapustyan, O. A. Капустян, О. А. |
| author_facet | Kapustyan, O. A. Капустян, О. А. |
| author_sort | Kapustyan, O. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:24:06Z |
| description | We consider the approximate optimal control based on the principle of feedback relation (synthesis) for a parabolic boundary-value problem. We represent the feedback operator as Fourier series in the eigenfunctions of the Laplace operator, which does not enable us to use these results in practice. In view of this fact, we justify the convergence of approximate controls, switching points, and values of the quality criterion to the exact values of the corresponding variables. |
| first_indexed | 2026-03-24T02:55:27Z |
| format | Article |
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| id | umjimathkievua-article-4210 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:55:27Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b5/2a32a7195556fb9225ed1d6bf29ba7b5.pdf |
| spelling | umjimathkievua-article-42102020-03-18T20:24:06Z Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem Наближений синтез оптимального обмеженого керування для параболічної крайової задачі Kapustyan, O. A. Капустян, О. А. We consider the approximate optimal control based on the principle of feedback relation (synthesis) for a parabolic boundary-value problem. We represent the feedback operator as Fourier series in the eigenfunctions of the Laplace operator, which does not enable us to use these results in practice. In view of this fact, we justify the convergence of approximate controls, switching points, and values of the quality criterion to the exact values of the corresponding variables. Розглянуто наближене оптимальне керування за принципом оберненої о зв'язку (синтезу) для параболічної крайової задачі. Оператор оберненої о зв'язку подається за допомогою рядів Фур'є за власними функціями оператора Лапласа, що не дозволяє використати ці результати для практичного застосування. У зв'язку з цим обі руніовусться збіжність наближених керувань, іочок перемикання, значень критерію якості до точних значень відповідних величин. Institute of Mathematics, NAS of Ukraine 2002-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4210 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 12 (2002); 1704-1709 Український математичний журнал; Том 54 № 12 (2002); 1704-1709 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4210/5127 https://umj.imath.kiev.ua/index.php/umj/article/view/4210/5128 Copyright (c) 2002 Kapustyan O. A. |
| spellingShingle | Kapustyan, O. A. Капустян, О. А. Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem |
| title | Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem |
| title_alt | Наближений синтез оптимального обмеженого керування для параболічної крайової задачі |
| title_full | Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem |
| title_fullStr | Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem |
| title_full_unstemmed | Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem |
| title_short | Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem |
| title_sort | approximate synthesis of optimal bounded control for a parabolic boundary-value problem |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4210 |
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