Splitting of two-point boundary problem appearing in the theory of optimal control
In a Hilbert space a two-point boundary-value problem is considered that arises during the minimization of a linear quadratic functional on the trajectories of a linear equation with the operator A + εB invertible for sufficiently small ε >0 for the derivative, where A is a Fredholm opera...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7969 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512839011139584 |
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| author | Kurina , G. A. Курина , Г. А. |
| author_facet | Kurina , G. A. Курина , Г. А. |
| author_sort | Kurina , G. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-12-01T10:43:23Z |
| description | In a Hilbert space a two-point boundary-value problem is considered that arises during the minimization of a linear quadratic functional on the trajectories of a linear equation with the operator A + εB invertible for sufficiently small ε >0 for the derivative, where A is a Fredholm operator and all B-Jordan chains of the operator A have the same length. It is proved that we can asymptotically split the problem under consideration into a regularly perturbed boundary-value problem and two singularity perturbed Cauchy problems. |
| first_indexed | 2026-03-24T03:35:09Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-7969 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:35:09Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e5/8dac222ff0419d031be6e17aa5d572e5.pdf |
| spelling | umjimathkievua-article-79692023-12-01T10:43:23Z Splitting of two-point boundary problem appearing in the theory of optimal control О расщеплении двухточечной краевой задачи, возникающей в теории оптимального управления Kurina , G. A. Курина , Г. А. In a Hilbert space a two-point boundary-value problem is considered that arises during the minimization of a linear quadratic functional on the trajectories of a linear equation with the operator A + εB invertible for sufficiently small ε >0 for the derivative, where A is a Fredholm operator and all B-Jordan chains of the operator A have the same length. It is proved that we can asymptotically split the problem under consideration into a regularly perturbed boundary-value problem and two singularity perturbed Cauchy problems. В гильбертовом пространстве рассматривается двухточечная краевая задача, возникающая при минимизации линейно-квадратичного функционала на траекториях линейного уравнения с обратимым при достаточно малых ε > 0 оператором А + εВ при производной, где оператор А фредгольмов, а все В-жордановы цепочки оператора А имеют одинаковую длину. Доказывается, что можно произвести асимптотическое расщепление рассматриваемой задачи на регулярно возмущенную краевую задачу и две сингулярно возмущенные задачи Коши. В гільбертовому просторі розглядається двоточкова крайова задача, що виникає при мінімізації лінійно-квадратичного функціоналу на траєкторіях лінійного рівняння з оберненим при досить малих ε > 0 оператором А + εВ при похідній, де оператор А фредгольмів, а всі В-жорданові ланцюжки оператора А мають однакову довжину. Доводиться, що можна виконати асимптотичне розщеплення розглядуваної задачі на регулярно збурену крайову задачу та дві сингулярно збурені задачі Коші.           Institute of Mathematics, NAS of Ukraine 1992-05-26 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7969 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 5 (1992); 704-709 Український математичний журнал; Том 44 № 5 (1992); 704-709 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7969/9562 Copyright (c) 1992 G. A. Kurina |
| spellingShingle | Kurina , G. A. Курина , Г. А. Splitting of two-point boundary problem appearing in the theory of optimal control |
| title | Splitting of two-point boundary problem appearing in the theory of optimal control |
| title_alt | О расщеплении двухточечной краевой задачи, возникающей в теории оптимального управления |
| title_full | Splitting of two-point boundary problem appearing in the theory of optimal control |
| title_fullStr | Splitting of two-point boundary problem appearing in the theory of optimal control |
| title_full_unstemmed | Splitting of two-point boundary problem appearing in the theory of optimal control |
| title_short | Splitting of two-point boundary problem appearing in the theory of optimal control |
| title_sort | splitting of two-point boundary problem appearing in the theory of optimal control |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7969 |
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