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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 1, Pages 199–222 (Mi timm538)  

This article is cited in 19 scientific papers (total in 19 papers)

On the question of the stability defect of sets in an approach game problem

V. N. Ushakov, A. G. Malev

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

Abstract: The stability property is studied in a game problem of the approach of a conflict-controlled system to a target set at a fixed termination time. The notion of the stability defect of sets in the space of game positions is investigated.

Keywords: approach game problem, control, conflict-controlled system, stable bridge, Hamiltonian.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 1, S229–S254

Bibliographic databases:

UDC: 517.977
Received: 20.11.2009

Citation: V. N. Ushakov, A. G. Malev, “On the question of the stability defect of sets in an approach game problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 199–222; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S229–S254

Citation in format AMSBIB
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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. Vladimir N. Ushakov, Aleksandr A. Uspenskii, “Defekt funktsii v differentsialnykh igrakh s terminalnoi platoi”, MTIP, 2:2 (2010), 99–128  mathnet  elib
    2. V. N. Ushakov, A. R. Matviichuk, P. D. Lebedev, “Defekt stabilnosti v igrovoi zadache o sblizhenii v moment”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 3, 87–103  mathnet  elib
    3. V. N. Ushakov, A. A. Uspenskii, “On a supplement to the stability property in differential games”, Proc. Steklov Inst. Math., 271 (2010), 286–305  mathnet  crossref  mathscinet  isi  elib
    4. V. N. Ushakov, A. A. Uspenskii, A. G. Malev, “Estimate of the stability defect for a positional absorption set subjected to discriminant transformations”, Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 113–129  mathnet  crossref  isi  elib
    5. 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
    6. 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  elib  scopus
    7. Ushakov V.N., Zimovets A.A., “Defekt invariantnosti mnozhestv otnositelno differentsialnogo vklyucheniya”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 16:4 (2011), 1201–1202  elib
    8. Ushakov V.N., Uspenskii A.A., Zimovets A.A., “Otsenka defekta stabilnosti deformatsii mnozhestva pozitsionnogo pogloscheniya v differentsialnoi igre sblizheniya-ukloneniya”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 16:4 (2011), 1203–1205  elib
    9. L. I. Rodina, “Statisticheskie kharakteristiki mnozhestva dostizhimosti i periodicheskie protsessy upravlyaemykh sistem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 2, 34–43  mathnet
    10. L. I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 2(40), 3–164  mathnet
    11. 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”, Proc. Steklov Inst. Math., 277 (2012), 266–277  mathnet  crossref  mathscinet  isi  elib  elib
    12. V. N. Ushakov, A. A. Zimovets, “K voprosu o slaboi invariantnosti mnozhestv otnositelno differentsialnogo vklyucheniya, porozhdennogo upravlyaemoi sistemoi”, Tr. IMM UrO RAN, 18, no. 4, 2012, 271–285  mathnet  elib
    13. A. G. Malev, “K voprosu ob otsenke defekta stabilnosti mnozhestv v igrovoi zadache o sblizhenii”, Tr. IMM UrO RAN, 19, no. 1, 2013, 205–216  mathnet  mathscinet  elib
    14. L. I. Rodina, “Estimation of statistical characteristics of attainability sets of controllable systems”, Russian Math. (Iz. VUZ), 57:11 (2013), 17–27  mathnet  crossref
    15. V. N. Ushakov, A. N. Kotel'nikova, A. G. Malev, “On estimation of the stability defect of the sets with piecewise smooth border”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 185–201  mathnet  crossref  mathscinet  isi  elib
    16. V. N. Ushakov, P. D. Lebedev, “Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 225–237  mathnet  crossref  mathscinet  isi  elib
    17. L. I. Rodina, A. Kh. Khammadi, “Kharakteristiki invariantnosti mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2016, no. 1(47), 44–53  mathnet  elib
    18. A. A. Chikrii, “Verkhnyaya i nizhnyaya razreshayuschie funktsii v igrovykh zadachakh dinamiki”, Tr. IMM UrO RAN, 23:1 (2017), 293–305  mathnet  crossref  elib
    19. V. N. Ushakov, V. I. Ukhobotov, A. E. Lipin, “An Addition to the Definition of a Stable Bridge and an Approximating System of Sets in Differential Games”, Proc. Steklov Inst. Math., 304 (2019), 268–280  mathnet  crossref  crossref  isi  elib
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