A numerical construction algorithm of Nash and Stackelberg solutions for two-person non-zero sum linear positional diffrential games
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
A numerical construction algorithm of Nash and Stackelberg solutions for two-person non-zero sum linear positional diffrential games
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| Автор |
Kleimenov, A. F.
Osipov, S. I. Kuvshinov, D. R. |
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| Тематика |
ALGORITHMS
COMPUTING DIFFRENTIAL GAMES NASH GAMES STACKELBERG GAMES TRAJECTORIES ALGORITHMS COMPUTATION THEORY COMPUTATIONAL GEOMETRY OPTIMAL CONTROL SYSTEMS TRAJECTORIES COMPUTATIONAL GEOMETRY ALGORITHMS COMPUTING CONSTRUCTION ALGORITHMS DIFFRENTIAL GAMES INTERSECTION OF POLYGONS NASH GAMES OPTIMAL CONTROL PROBLEM STACKELBERG GAMES COMPUTER GAMES |
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| Описание |
The report evolves a method, which uses the formalization and results of positional antagonistic diérential games theory, developed by N. N. Krasovskii and his scientific school, for constructing solutions of a class of non-antagonistic diérential games. The method transforms non-antagonistic game into so-called non-standard optimal control problem. Numerical solutions for Stackelberg games are constructed by an algorithm developed by S. Osipov. Numerical Nash solution construction algorithm based upon auxiliary bimatrix games sequence is presented. Used computational geometry algorithms include convex hull construction, union and intersection of polygons and a Minkowski sum for polygons. Results of numerical experiment for a material point motion in plane are presented. The point is moved by force formed by two players. Every player has his personal target point. Among the obtained results, there is a Nash solution such that along the corresponding trajectory the position of the game is non-antagonistic, at first, and then becomes globally antagonistic starting from some moment of time.
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| Дата |
2024-04-24T12:38:28Z
2024-04-24T12:38:28Z 2009 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Kleimenov, A. F., Osipov, S. I., & Kuvshinov, D. R. (2009). A numerical construction algorithm of Nash and stackelberg solutions for two-person non-zero sum linear positional differential games. IFAC Proceedings Volumes, 42(2), 193–198. doi:10.3182/20090506-3-sf-4003.00036
978-3-90266142-5 1474-6670 Final All Open Access, Bronze https://doi.org/10.3182/20090506-3-sf-4003.00036 http://elar.urfu.ru/handle/10995/132618 10.3182/20090506-3-sf-4003.00036 84941985594 000362569400023 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Elsevier BV
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| Источник |
IFAC Proceedings Volumes
IFAC Proceedings Volumes (IFAC-PapersOnline) |
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