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Tr. Mat. Inst. Steklova, 2012, Volume 277, Pages 275–287 (Mi tm3388)  

This article is cited in 4 scientific papers (total in 4 papers)

Differential games with fixed terminal time and estimation of the instability degree of sets in these games

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

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

Abstract: This paper contributes to the theory of differential games. A game problem of bringing a conflict-controlled system to a compact target set is analyzed. Sets in the position space that terminate on the target set and are not stable bridges are considered. The notion of stability defect of these sets is examined. It is demonstrated how the notion of stability defect can be used to construct sets with relatively good geometry that are at the same time convenient for the first player to play the game successfully.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 277, 266–277

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received in January 2012

Citation: V. N. Ushakov, P. D. Lebedev, A. R. Matviychuk, A. G. Malev, “Differential games with fixed terminal time and estimation of the instability degree of sets in these games”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Tr. Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 275–287; Proc. Steklov Inst. Math., 277 (2012), 266–277

Citation in format AMSBIB
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\paper Differential games with fixed terminal time and estimation of the instability degree of sets in these games
\inbook Mathematical control theory and differential equations
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko
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\pages 275--287
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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. 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
    2. 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
    3. V. N. Ushakov, A. R. Matviychuk, A. V. Ushakov, “On one algorithm for solution to the control problem using sets of guides”, Application of Mathematics in Technical and Natural Sciences, AIP Conf. Proc., 1895, ed. M. Todorov, Amer. Inst. Phys., 2017, UNSP 110008-1  crossref  isi
    4. A. E. Lamotkin, S. I. Osipov, “Issledovanie igrovoi zadachi tormozheniya diska v sluchae postoyannykh upravlenii”, Tr. IMM UrO RAN, 25, no. 1, 2019, 93–107  mathnet  crossref  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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