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http://elar.urfu.ru/handle/10995/95294
Название: | Pursuit-Evasion Differential Games with the Grönwall Type Constraints on Controls |
Авторы: | Samatov, Bahrom T. Ibragimov, Gafurjan Khodjibayeva, Iroda V. |
Дата публикации: | 2020 |
Издатель: | N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences Ural Federal University named after the first President of Russia B.N. Yeltsin |
Библиографическое описание: | Samatov B. T. Pursuit-Evasion Differential Games with the Grönwall Type Constraints on Controls / Bahrom T. Samatov, Gafurjan Ibragimov, Iroda V. Khodjibayeva. — DOI 10.15826/umj.2020.2.010. — Text : electronic // Ural Mathematical Journal. — 2020. — Volume 6. — № 2. — С. 95-107. |
Аннотация: | A simple pursuit-evasion differential game of one pursuer and one evader is studied. The players' controls are subject to differential constraints in the form of the integral Grönwall inequality. The pursuit is considered completed if the state of the pursuer coincides with the state of the evader. The main goal of this work is to construct optimal strategies for the players and find the optimal pursuit time. A parallel approach strategy for Grönwall-type constraints is constructed and it is proved that it is the optimal strategy of the pursuer. In addition, the optimal strategy of the evader is constructed and the optimal pursuit time is obtained. The concept of a parallel pursuit strategy (Π-strategy for short) was introduced and used to solve the quality problem for "life-line" games by L.A.Petrosjan. This work develops and expands the works of Isaacs, Petrosjan, Pshenichnyi, and other researchers, including the authors. |
Ключевые слова: | DIFFERENTIAL GAME GRÖNWALL'S INEQUALITY GEOMETRIC CONSTRAINT PURSUIT EVASION OPTIMAL STRATEGY DOMAIN OF ATTAINABILITY LIFE-LINE |
URI: | http://elar.urfu.ru/handle/10995/95294 |
Условия доступа: | Creative Commons Attribution License |
Текст лицензии: | https://creativecommons.org/licenses/by/4.0/ |
ISSN: | 2414-3952 |
DOI: | 10.15826/umj.2020.2.010 |
Сведения о поддержке: | The present research was partially supported by the National Fundamental Research Grant Scheme FRGS of Malaysia (Project No.01-01-17-1921FR) and by the National Fundamental Research Grant Scheme of the National University Uzbekistan (Project No.FR-GS-33). |
Источники: | Ural Mathematical Journal. 2020. Volume 6. № 2 |
Располагается в коллекциях: | Ural Mathematical Journal |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
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umj_2020_6_2_95-107.pdf | 185,19 kB | Adobe PDF | Просмотреть/Открыть |
Лицензия на ресурс: Лицензия Creative Commons