
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 2, Pages 197–211
(Mi vuu477)




This article is cited in 2 scientific papers (total in 2 papers)
MATHEMATICS
Singletype problem of pulse meeting in fixed time with terminal set in 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 the fixed end time $p$. Attainability domains of players are $n$dimensional balls. The terminal set of a game is determined by a condition for assigning the norm of a phase vector to a segment with positive ends. A set defined by this condition is named in the article as ring. The fact that the terminal set is not convex required an additional theory allowing us to calculate Minkowski sum and difference for a ring and a ball in $n$dimensional space.
Control of the first player has a pulse constraint. Abilities of the first player are determined by the stock of resources that can be used by the player at formation of his control. At certain moments of time the separation of a part of the resources stock is possible, which may implicate an “instantaneous” change of a phase vector, thereby complicating the problem. Control of the second player has geometrical constraints.
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.
The maximal stable bridge leading at fixed time to the terminal set has been constructed. A stable bridge is determined by the functions of internal and external radii, which are calculated explicitly.
Keywords:
pulse control, differential game, stable bridge.
Full text:
PDF file (249 kB)
References:
PDF file
HTML file
UDC:
517.977.80
MSC: 91A23, 49N75 Received: 28.04.2015
Citation:
V. I. Ukhobotov, I. V. Izmest'ev, “Singletype problem of pulse meeting in fixed time with terminal set in form of a ring”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:2 (2015), 197–211
Citation in format AMSBIB
\Bibitem{UkhIzm15}
\by V.~I.~Ukhobotov, I.~V.~Izmest'ev
\paper Singletype problem of pulse meeting in fixed time with terminal set in form of a ring
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 2
\pages 197211
\mathnet{http://mi.mathnet.ru/vuu477}
\elib{http://elibrary.ru/item.asp?id=23681102}
Linking options:
http://mi.mathnet.ru/eng/vuu477 http://mi.mathnet.ru/eng/vuu/v25/i2/p197
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:

V. I. Ukhobotov, I. V. Izmestev, “Sintez upravlenii v odnotipnoi igrovoi zadache impulsnoi vstrechi v zadannyi moment vremeni s terminalnym mnozhestvom v forme koltsa”, Vestn. Udmurtsk. unta. Matem. Mekh. Kompyut. nauki, 27:1 (2017), 69–85

V. N. Ushakov, A. A. Ershov, G. V. Parshikov, “O privedenii dvizheniya upravlyaemoi sistemy na mnozhestvo Lebega lipshitsevoi funktsii”, Vestn. Udmurtsk. unta. Matem. Mekh. Kompyut. nauki, 28:4 (2018), 489–512

Number of views: 
This page:  264  Full text:  105  References:  64 
