ПРО НЕСТАЦІОНАРНУ ЗАДАЧУ КЕРУВАННЯ РУХОМ У КОНФЛІКТНІЙ СИТУАЦІЇ
Mathematical theory of control under conflict and uncertainty provides a wide range of fundamental methods to study controlled dynamic processes of various nature. In this paper the game problems of pursuit for nonstationary controlled processes ofgeneral type with cylindrical terminal set are consi...
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| Дата: | 2025 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2025
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| Теми: | |
| Онлайн доступ: | https://jais.net.ua/index.php/files/article/view/670 |
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| Назва журналу: | Problems of Control and Informatics |
Репозитарії
Problems of Control and Informatics| Резюме: | Mathematical theory of control under conflict and uncertainty provides a wide range of fundamental methods to study controlled dynamic processes of various nature. In this paper the game problems of pursuit for nonstationary controlled processes ofgeneral type with cylindrical terminal set are considered. The investigation is closely related with the L.S. Pontryagin first direct method and the method of resolving functions. The purpose of the paper is to derive sufficient conditions for the gametermination for some guaranteed time in favour of the first player and to provide the control realizing this result. In the development of the method of resolving functions, the upper and the lower resolving functions of two types are introduced in the formof support functions of special set-valued mappings. This made it possible to deduce conditions for the game termination in the class of quasi- and stroboscopic strategies. The in-depth analysis of properties of the special set-valued mappings and theirselections, around which measurable controls are chosen by virtue of the measurable choice theorem, is provided. A comparison of the guaranteed times of the abovementioned method is given. In so doing, the L×B-measurability of key set-valued mappings and corresponding resolving functions — the support functions of these mappings, is used. The property for superpositional measurability of above mentioned objects plays essential role in the method design. In specific model examples, as a rule, the resolving functions are the greatest positive roots of certain quadratic equations that makes it possible to obtain solution in an analytic form. |
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