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MATHEMATICS
On a discrete game problem with non-convex control vectograms
I. V. Izmestyevab, V. I. Ukhobotovba a Chelyabinsk State University, ul. Brat'ev
Kashirinykh, 129, Chelyabinsk, 454001, Russia
b Institute of Mathematics and
Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg,
620219, Russia
Abstract:
In a normed space of finite dimension, a discrete game problem with fixed duration is considered. The terminal set is determined by the condition that the norm of the phase vector belongs to a segment with positive ends. In this paper, a set defined by this condition is called a ring. At each moment, the vectogram of the first player's controls is a certain ring. The controls of the second player at each moment are taken from balls with given radii. The goal of the first player is to lead a phase vector to the terminal set at a fixed time. The goal of the second player is the opposite. In this paper, necessary and sufficient termination conditions are found, and optimal controls of the players are constructed.
Keywords:
game, control, vectogram, terminal set.
Received: 03.11.2021
Citation:
I. V. Izmestyev, V. I. Ukhobotov, “On a discrete game problem with non-convex control vectograms”, Izv. IMI UdGU, 58 (2021), 48–58
Linking options:
https://www.mathnet.ru/eng/iimi420 https://www.mathnet.ru/eng/iimi/v58/p48
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Abstract page: | 191 | Full-text PDF : | 77 | References: | 21 |
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