Geodesic
On a discrete game problem with non-convex control vectograms
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 58 (2021), pp. 48-58

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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. 
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     author = {I. V. Izmestyev and V. I. Ukhobotov},
     title = {On a discrete game problem with non-convex control vectograms},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {48--58},
     publisher = {mathdoc},
     volume = {58},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2021_58_a2/}
}
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I. V. Izmestyev; V. I. Ukhobotov. On a discrete game problem with non-convex control vectograms. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 58 (2021), pp. 48-58. http://geodesic.mathdoc.fr/item/IIMI_2021_58_a2/