Conditions of unique solvability for the inverse problems in controlled dynamical systems
Problems arising in the applications of control theory of dynamical systems, when part of the variables of the mathematical model of the system is unknown and is subject to determination from information on the output of the system, are considered. Fundamental among them are the observation and iden...
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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/8232 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512988775055360 |
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| author | Kovalev, A. M. Shcherbak, V. F. Ковалев, А. М. Щербак, В. Ф. |
| author_facet | Kovalev, A. M. Shcherbak, V. F. Ковалев, А. М. Щербак, В. Ф. |
| author_sort | Kovalev, A. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-03-27T09:55:23Z |
| description | Problems arising in the applications of control theory of dynamical systems, when part of the variables of the mathematical model of the system is unknown and is subject to determination from information on the output of the system, are considered. Fundamental among them are the observation and identification problems, when unknown are the state of the system and its parameters, respectively, and also the problem of inverting the system, in which one seeks the control. Based on an analysis of mappings that are generated by an extended measurement vector, conditions for the unique solvability of the afore–mentioned problems with respect to a single trajectory or a set of trajectories are obtained. |
| first_indexed | 2026-03-24T03:37:32Z |
| format | Article |
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| id | umjimathkievua-article-8232 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:37:32Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/87/7bb454aee1152ef8050c1bb7b050d887.pdf |
| spelling | umjimathkievua-article-82322024-03-27T09:55:23Z Conditions of unique solvability for the inverse problems in controlled dynamical systems Условия однозначной разрешимости обратных задач управляемых динамических систем Kovalev, A. M. Shcherbak, V. F. Ковалев, А. М. Щербак, В. Ф. Problems arising in the applications of control theory of dynamical systems, when part of the variables of the mathematical model of the system is unknown and is subject to determination from information on the output of the system, are considered. Fundamental among them are the observation and identification problems, when unknown are the state of the system and its parameters, respectively, and also the problem of inverting the system, in which one seeks the control. Based on an analysis of mappings that are generated by an extended measurement vector, conditions for the unique solvability of the afore–mentioned problems with respect to a single trajectory or a set of trajectories are obtained. Рассмотрены задачи, возникающие в приложениях теории управления динамических систем, когда часть переменных математической модели объекта неизвестна и подлежит определению по информации о выходе системы. Основными среди них являются задачи наблюдения и идентификации, где неизвестны соответственно состояние системы и ее параметры, а также задача обращения системы, в которой ищется управление. На основе анализа отображений, порожденных расширенным вектором измерений, получены условия однозначной разрешимости указанных задач по одной и по множеству траекторий. Розглянуті задачі, що виникають в застосуваннях теорії керування динамічних систем, коли частина змінних математичної моделі об’єкта невідома і підлягає визначенню за інформацією про вихід системи. Основними серед них є задачі спостереження та ідентифікації, де невідомі відповідно стан системи та її параметри, а також задача обернення системи, в якій шукається керування. На основі аналізу відображень, породжених розширеним вектором вимірювань, одержані умови однозначної розв’язності вказаних задач за однією і за множиною траєкторій. Institute of Mathematics, NAS of Ukraine 1992-10-01 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8232 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 10 (1992); 1359-1366 Український математичний журнал; Том 44 № 10 (1992); 1359-1366 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8232/9812 Copyright (c) 1992 A. M. Kovalev, V. F. Shcherbak |
| spellingShingle | Kovalev, A. M. Shcherbak, V. F. Ковалев, А. М. Щербак, В. Ф. Conditions of unique solvability for the inverse problems in controlled dynamical systems |
| title | Conditions of unique solvability for the inverse problems in controlled dynamical systems |
| title_alt | Условия однозначной разрешимости обратных задач управляемых динамических систем |
| title_full | Conditions of unique solvability for the inverse problems in controlled dynamical systems |
| title_fullStr | Conditions of unique solvability for the inverse problems in controlled dynamical systems |
| title_full_unstemmed | Conditions of unique solvability for the inverse problems in controlled dynamical systems |
| title_short | Conditions of unique solvability for the inverse problems in controlled dynamical systems |
| title_sort | conditions of unique solvability for the inverse problems in controlled dynamical systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8232 |
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