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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 1, Pages 40–51 (Mi timm526)  

This article is cited in 25 scientific papers (total in 25 papers)

On a nonstationary problem of group pursuit

A. S. Bannikov, N. N. Petrov

Udmurt State University

Abstract: Pontryagin's classical nonstationary example with many participants and phase constraints on the evader's states with equal dynamic and inertia capabilities of the players is considered. The case of a simple motion is considered separately. Solvability conditions for problems of pursuit and evasion are obtained.

Keywords: group pursuit, nonstationary problem, Pontryagin's example, phase constraints.

Full text: PDF file (192 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 271, suppl. 1, S41–S52

Bibliographic databases:

UDC: 517.977
Received: 11.01.2010

Citation: A. S. Bannikov, N. N. Petrov, “On a nonstationary problem of group pursuit”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 40–51; Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S41–S52

Citation in format AMSBIB
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\paper On a~nonstationary problem of group pursuit
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 16
\issue 1
\pages 40--51
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 271
\issue , suppl. 1
\pages S41--S52
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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. Nikolay N. Petrov, “To the non-stationary problem of the group pursuit with phase restrictions”, Autom. Remote Control, 75:8 (2014), 1525–1531  mathnet  crossref
    2. A. S. Bannikov, “O zadache pozitsionnoi poimki odnogo ubegayuschego gruppoi presledovatelei”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 1, 3–7  mathnet
    3. Nadezhda A. Soloveva, “Odna zadacha gruppovogo presledovaniya v lineinykh rekurrentnykh differentsialnykh igrakh”, MTIP, 3:1 (2011), 81–90  mathnet
    4. M. N. Vinogradova, “O poimke dvukh ubegayuschikh v zadache prostogo presledovaniya s fazovymi ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 4, 3–8  mathnet
    5. D. V. Sakharov, “O dvukh differentsialnykh igrakh prostogo gruppovogo presledovaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 1, 50–59  mathnet
    6. Marina N. Vinogradova, “O poimke dvukh ubegayuschikh v nestatsionarnoi zadache prostogo presledovaniya”, MTIP, 4:1 (2012), 21–31  mathnet
    7. M. N. Vinogradova, “O poimke dvukh ubegayuschikh v zadache prostogo presledovaniya”, Izv. IMI UdGU, 2012, no. 1(39), 26–27  mathnet
    8. E. V. Kotlyachkova, “Prostoe gruppovoe presledovanie v klasse impulsnykh strategii”, Izv. IMI UdGU, 2012, no. 1(39), 69–70  mathnet
    9. N. N. Petrov, N. A. Soloveva, “Gruppovoe presledovanie v rekurrentnykh differentsialnykh igrakh”, Izv. IMI UdGU, 2012, no. 1(39), 99–100  mathnet
    10. E. V. Kotlyachkova, “Prostoe presledovanie s fazovymi ogranicheniyami v klasse impulsnykh strategii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 3, 48–52  mathnet
    11. Denis V. Sakharov, “Odna zadacha gruppovogo presledovaniya v lineinoi pochti periodicheskoi differentsialnoi igre”, MTIP, 4:3 (2012), 86–100  mathnet
    12. N. N. Petrov, K. A. Schelchkov, “K zadache Chernousko”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 62–67  mathnet
    13. Petrov N.N., Solov'eva N.A., “Problem of Pursuit of a Group of Coordinated Evaders in Linear Recurrent Differential Games”, J. Comput. Syst. Sci. Int., 51:6 (2012), 770–778  crossref  mathscinet  zmath  isi  elib  elib
    14. M. N. Vinogradova, N. N. Petrov, N. A. Soloveva, “Poimka dvukh skoordinirovannykh ubegayuschikh v lineinykh rekurrentnykh differentsialnykh igrakh”, Tr. IMM UrO RAN, 19, no. 1, 2013, 41–48  mathnet  mathscinet  elib
    15. A. S. Bannikov, “Nekotorye nestatsionarnye zadachi gruppovogo presledovaniya”, Izv. IMI UdGU, 2013, no. 1(41), 3–46  mathnet
    16. D. V. Sakharov, “Odna zadacha gruppovogo presledovaniya v primere Pontryagina”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 125–131  mathnet
    17. N. A. Soloveva, “Gruppovoe presledovanie v rekurrentnom primere L. S. Pontryagina”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 3, 83–89  mathnet
    18. M. N. Vinogradova, “O poimke dvukh ubegayuschikh v odnoi nestatsionarnoi zadache gruppovogo presledovaniya s fazovymi ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 12–20  mathnet  elib
    19. N. N. Petrov, N. A. Solov'eva, “Multiple capture in Pontryagin's recursive example with phase constraints”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 174–182  mathnet  crossref  mathscinet  isi  elib
    20. E. V. Kotlyachkova, “K nestatsionarnoi zadache prostogo presledovaniya v klasse impulsnykh strategii”, Izv. IMI UdGU, 2015, no. 1(45), 106–113  mathnet  elib
    21. A. I. Blagodatskikh, N. N. Petrov, “Group Pursuit With State Constraints in Pontryagin's Almost Periodic Example”, Differ. Equ., 51:3 (2015), 391–398  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    22. N. N. Petrov, N. A. Solov'eva, “Multiple capture in Pontryagin's recurrent example”, Autom. Remote Control, 77:5 (2016), 855–861  mathnet  crossref  isi  elib  elib
    23. N. N. Petrov, N. A. Soloveva, “Mnogokratnaya poimka ubegayuschego v lineinykh rekurrentnykh differentsialnykh igrakh”, Tr. IMM UrO RAN, 23:1 (2017), 212–218  mathnet  crossref  elib
    24. G. Ibragimov, M. Ferrara, A. Kuchkarov, B. A. Pansera, “Simple Motion Evasion Differential Game of Many Pursuers and Evaders With Integral Constraints”, Dyn. Games Appl., 8:2 (2018), 352–378  crossref  mathscinet  zmath  isi  scopus
    25. A. Ya. Narmanov, K. A. Schelchkov, “Zadacha ukloneniya v nelineinoi differentsialnoi igre s diskretnym upravleniem”, Izv. IMI UdGU, 52 (2018), 75–85  mathnet  crossref  elib
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