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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, Issue 3, Pages 87–103 (Mi vuu170)  

This article is cited in 10 scientific papers (total in 10 papers)

MATHEMATICS

Defect of stability in game-pursuit problem

V. N. Ushakov, A. R. Matviychuk, P. D. Lebedev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The article is about the sets in the phase space of a game-pursuit problem, which are not stable in general. Conception of the stability defect is researched. The sets with simple geometry are constructed based on the stability defect, the extremal aiming on them provides the achieving of the goal set neighborhood for the first player.

Keywords: game pursuit problem, stable bridge, Hamiltonian, stability defect of the set.

Full text: PDF file (569 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.917
MSC: 37C75
Received: 01.03.2010

Citation: V. N. Ushakov, A. R. Matviychuk, P. D. Lebedev, “Defect of stability in game-pursuit problem”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3, 87–103

Citation in format AMSBIB
\Bibitem{UshMatLeb10}
\by V.~N.~Ushakov, A.~R.~Matviychuk, P.~D.~Lebedev
\paper Defect of stability in game-pursuit problem
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2010
\issue 3
\pages 87--103
\mathnet{http://mi.mathnet.ru/vuu170}
\elib{http://elibrary.ru/item.asp?id=15112953}


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    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. N. Ushakov, A. A. Zimovets, “Defekt invariantnosti mnozhestv otnositelno differentsialnogo vklyucheniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 2, 98–111  mathnet
    2. V. N. Ushakov, A. R. Matviichuk, A. V. Ushakov, “Approksimatsiya mnozhestv dostizhimosti i integralnykh voronok differentsialnykh vklyuchenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 4, 23–39  mathnet
    3. Ushakov V.N., “On the Stability Property in a Game-Theoretic Approach Problem with Fixed Terminal Time”, Differ. Equ., 47:7 (2011), 1046–1058  crossref  mathscinet  zmath  isi  elib  scopus
    4. P. D. Lebedev, A. V. Ushakov, “Approximating sets on a plane with optimal sets of circles”, Autom. Remote Control, 73:3 (2012), 485–493  mathnet  crossref  isi
    5. A. A. Usova, “Ob asimptoticheskikh svoistvakh optimalnykh reshenii i funktsii tseny v zadachakh optimalnogo upravleniya na beskonechnom gorizonte”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 1, 77–95  mathnet
    6. L. I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 2(40), 3–164  mathnet
    7. P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Algoritmy nailuchshei approksimatsii ploskikh mnozhestv ob'edineniyami krugov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 88–99  mathnet
    8. P. D. Lebedev, D. S. Bukharov, “Approksimatsiya mnogougolnikov nailuchshimi naborami krugov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:3 (2013), 72–87  mathnet
    9. V. N. Ushakov, A. S. Lakhtin, P. D. Lebedev, “Optimization of the Hausdorff distance between sets in Euclidean space”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 222–238  mathnet  crossref  mathscinet  isi  elib
    10. V. N. Ushakov, P. D. Lebedev, “Algoritmy optimalnogo pokrytiya mnozhestv na ploskosti $\mathbb{R}^2$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:2 (2016), 258–270  mathnet  crossref  mathscinet  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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