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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 1, Pages 69–85 (Mi vuu570)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Synthesis of controls in a single-type game problem of pulse meeting at fixed time with a terminal set in the form of a ring

V. I. Ukhobotov, I. V. Izmest'ev

Chelyabinsk State University, ul. Brat'ev Kashirinykh, 129, Chelyabinsk, 454001, Russia

Abstract: We consider a linear differential game with a pulse control of the first player. The abilities of the first player are determined by the stock of resources that the player can use when forming his control. At certain instants of time a separation of part of the resources stock is possible, which may implicate an “instantaneous” change of a phase vector, resulting in the complication of the problem. The control of the second player has geometrical constraints. The vectograms of the players are described by the same ball with different time-dependent radii. The terminal set of the game is determined by the condition of belonging the norm of a phase vector to a segment with positive ends. In this paper, a set defined by this condition is called a ring. The aim of the first player is to lead a phase vector to the terminal set at fixed time. The aim of the second player is opposite. With the maximal stable bridge, which has been defined by the authors previously, optimal controls of players are constructed.

Keywords: pulse control, optimal control, differential game.

DOI: https://doi.org/10.20537/vm170107

Full text: PDF file (371 kB)
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Bibliographic databases:

UDC: 517.977.80
MSC: 91A23, 49N75
Received: 12.12.2016

Citation: V. I. Ukhobotov, I. V. Izmest'ev, “Synthesis of controls in a single-type game problem of pulse meeting at fixed time with a terminal set in the form of a ring”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017), 69–85

Citation in format AMSBIB
\Bibitem{UkhIzm17}
\by V.~I.~Ukhobotov, I.~V.~Izmest'ev
\paper Synthesis of controls in a single-type game problem of pulse meeting at fixed time with a terminal set in the form of a ring
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 1
\pages 69--85
\mathnet{http://mi.mathnet.ru/vuu570}
\crossref{https://doi.org/10.20537/vm170107}
\elib{http://elibrary.ru/item.asp?id=28808557}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Ukhobotov, I. S. Stabulit, “Dinamicheskaya zadacha upravleniya pri nalichii pomekhi i s zadannym mnozhestvom momentov korrektsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 74–81  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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