RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

Single-type 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, “Single-type 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 Single-type 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 197--211
\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

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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:
    1. 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. un-ta. Matem. Mekh. Kompyut. nauki, 27:1 (2017), 69–85  mathnet  crossref  elib
    2. V. N. Ushakov, A. A. Ershov, G. V. Parshikov, “O privedenii dvizheniya upravlyaemoi sistemy na mnozhestvo Lebega lipshitsevoi funktsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:4 (2018), 489–512  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:264
    Full text:105
    References:64

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020