Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika"
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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2018, Volume 10, Issue 4, Pages 41–48
DOI: https://doi.org/10.14529/mmph180405 (Mi vyurm391) 		 
Mathematics

On a game problem for point control near the surface of the Moon

V. I. Ukhobotov, P. I. Maksakova

Chelyabinsk State University, Chelyabinsk, Russian Federation
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DOI: https://doi.org/10.14529/mmph180405
Abstract: A game control problem in which the first player controls the material point of variable composition is considered. The second player controls the point that can move with a limited speed. It is assumed that the material point of variable composition, along with the controlled reactive power, is exposed to a constant force, the value of which is proportional to the mass of the point. This situation occurs, for example, when we consider the motion of a material point near the surface of the Moon, where there is no atmospheric resistance. It is considered that the point of variable composition has constant relative velocity of separating fuel particles, and the value of thrust is limited from above with a given positive number. The first player tries to minimize the distance between the points in a set moment, consuming as little resources as possible. The formulated two-criterion problem, with the use of weight coefficients, gets reduced to a differential game, the payoff of which is the sum of both terminal and integral components. By changing variables, the problem is reduced to a single-type game in which vectograms of players are balls with time-dependent radii. The function of the game price is calculated, and optimal control of the players is determined.
Keywords: control, differential game, payoff.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00264_a
Received: 14.05.2018
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: V. I. Ukhobotov, P. I. Maksakova, “On a game problem for point control near the surface of the Moon”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018), 41–48
Citation in format AMSBIB
\Bibitem{UkhMak18}
\by V.~I.~Ukhobotov, P.~I.~Maksakova
\paper On a game problem for point control near the surface of the Moon
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2018
\vol 10
\issue 4
\pages 41--48
\mathnet{http://mi.mathnet.ru/vyurm391}
\crossref{https://doi.org/10.14529/mmph180405}
\elib{https://elibrary.ru/item.asp?id=36313215}
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