Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem
An extension of the solution set of the finite-time stabilization problem by bounded feedback controls, which is also called the synthesis problem for the canonical system via Korobov's nonunique controllability function, is given. We consider the case when the value of the controllability func...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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oai:jmag.ilt.kharkiv.ua:article-10212023-11-29T18:04:11Z Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem Choque-Rivero, A. E. проблема синтезу стабiлiзацiя за скiнченний час обмежене керування канонiчна система synthesis problem finite-time stabilization bounded control controllability function canonical system An extension of the solution set of the finite-time stabilization problem by bounded feedback controls, which is also called the synthesis problem for the canonical system via Korobov's nonunique controllability function, is given. We consider the case when the value of the controllability functions at the initial point is exactly the time of motion from the initial point to the origin. The family of positional controls resolving the synthesis problem is given in terms of a certain real parameter. We enlarge the interval of the parameters and explicitly compute its endpoints as functions of the dimension $n$ of the given system. Mathematical Subject Classification 2020: 93D15, 34D20, 34D05, 34H05. Знайдено розширення множини розв’язкiв проблеми стабiлiзацiї за скiнченний час за допомогою обмеженого позицiйного керування, яка також називається проблемою синтезу для канонiчної системи за допомогою функцiї керованостi Коробова. Ми розглядаємо випадок, коли значення функцiй керованостi в початковiй точцi є часом руху з цiєї початкової точки до нуля. У термiнах певних реальних параметрiв знайдено сiм’ю позицiйних керувань, що розв’язують проблему синтезу. Ми збiльшуємо iнтервал параметрiв i явно обчислюємо його кiнцевi точки як функцiї вiд розмiрностi $n$ системи, що розглядається. Mathematical Subject Classification 2020: 93D15, 34D20, 34D05, 34H05. Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2023-11-29 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1021 10.15407/mag19.03.556 Journal of Mathematical Physics, Analysis, Geometry; Vol. 19 No. 3 (2023); 556-586 Журнал математической физики, анализа, геометрии; Том 19 № 3 (2023); 556-586 Журнал математичної фізики, аналізу, геометрії; Том 19 № 3 (2023); 556-586 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1021/jm19-0556e Авторське право (c) 2023 Журнал математичної фізики, аналізу, геометрії |
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Journal of Mathematical Physics, Analysis, Geometry |
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| datestamp_date |
2023-11-29T18:04:11Z |
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OJS |
| language |
English |
| topic |
проблема синтезу стабiлiзацiя за скiнченний час обмежене керування канонiчна система |
| spellingShingle |
проблема синтезу стабiлiзацiя за скiнченний час обмежене керування канонiчна система Choque-Rivero, A. E. Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem |
| topic_facet |
проблема синтезу стабiлiзацiя за скiнченний час обмежене керування канонiчна система synthesis problem finite-time stabilization bounded control controllability function canonical system |
| format |
Article |
| author |
Choque-Rivero, A. E. |
| author_facet |
Choque-Rivero, A. E. |
| author_sort |
Choque-Rivero, A. E. |
| title |
Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem |
| title_short |
Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem |
| title_full |
Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem |
| title_fullStr |
Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem |
| title_full_unstemmed |
Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem |
| title_sort |
korobov’s controllability function as motion time: extension of the solution set of the synthesis problem |
| title_alt |
Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem Korobov’s Controllability Function as Motion Time: Extension of the Solution Set of the Synthesis Problem |
| description |
An extension of the solution set of the finite-time stabilization problem by bounded feedback controls, which is also called the synthesis problem for the canonical system via Korobov's nonunique controllability function, is given. We consider the case when the value of the controllability functions at the initial point is exactly the time of motion from the initial point to the origin. The family of positional controls resolving the synthesis problem is given in terms of a certain real parameter. We enlarge the interval of the parameters and explicitly compute its endpoints as functions of the dimension $n$ of the given system.
Mathematical Subject Classification 2020: 93D15, 34D20, 34D05, 34H05. |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2023 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1021 |
| work_keys_str_mv |
AT choqueriveroae korobovscontrollabilityfunctionasmotiontimeextensionofthesolutionsetofthesynthesisproblem |
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2025-09-26T01:40:38Z |
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2025-09-26T01:40:38Z |
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1850836703997067264 |