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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 2, Pages 178–186 (Mi timm1180)  

This article is cited in 12 scientific papers (total in 12 papers)

Multiple capture in Pontryagin's recursive example with phase constraints

N. N. Petrov, N. A. Solov'eva

Udmurt State University, Mathematical Department
References:
Abstract: We consider Pontryagin's generalized nonstationary example with identical dynamic and inertial capabilities of the players and state constraints on the evader's states. The boundary of the phase constraints is not a “death line” for the evader. The set of admissible controls is a ball centered at the origin, and the terminal sets are the origin. We obtain sufficient conditions for a multiple capture of one evader by a group of pursuers in the case when some functions corresponding to the initial data and parameters of the game are recursive.
Keywords: pursuer, evader, phase restrictions, Pontryagin's example, group pursuit.
Received: 10.02.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 293, Issue 1, Pages 174–182
DOI: https://doi.org/10.1134/S0081543816050163
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: N. N. Petrov, N. A. Solov'eva, “Multiple capture in Pontryagin's recursive example with phase constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 178–186; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 174–182
Citation in format AMSBIB
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\vol 21
\issue 2
\pages 178--186
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\issue , suppl. 1
\pages 174--182
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Linking options:
  • https://www.mathnet.ru/eng/timm1180
  • https://www.mathnet.ru/eng/timm/v21/i2/p178
  • This publication is cited in the following 12 articles:
    1. A. I. Blagodatskikh, “Sinkhronnaya realizatsiya odnovremennykh mnogokratnykh poimok ubegayuschikh”, Izv. IMI UdGU, 61 (2023), 3–26  mathnet  crossref
    2. K. A. Shchelchkov, “Relative optimality in nonlinear differential games with discrete control”, Sb. Math., 214:9 (2023), 1337–1350  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. K. A. Shchelchkov, “One-Sided Capture in Nonlinear Differential Games”, Int. Game Theory Rev., 25:02 (2023)  crossref
    4. Shchelchkov K., “Epsilon-Capture in Nonlinear Differential Games Described By System of Order Two”, Dyn. Games Appl., 12:2 (2022), 662–676  crossref  mathscinet  isi  scopus
    5. Alena I. Machtakova, Nikolai N. Petrov, “Matrix resolving functions in the linear group pursuit problem with fractional derivatives”, Ural Math. J., 8:1 (2022), 76–89  mathnet  crossref  mathscinet
    6. K. A. Shchelchkov, “Estimate of the Capture Time and Construction of the Pursuer's Strategy in a Nonlinear Two-Person Differential Game”, Diff Equat, 58:2 (2022), 264  crossref
    7. N. N. Petrov, N. A. Solov'eva, “Multiple capture of given number of evaders in linear recurrent differential games”, J. Optim. Theory Appl., 182:1, SI (2019), 417–429  crossref  isi
    8. N. N. Petrov, “Group pursuit problem in a differential game with fractional derivatives, state constraints, and simple matrix”, Differ. Equ., 55:6 (2019), 841–848  crossref  mathscinet  zmath  isi  scopus
    9. N. N. Petrov, “A multiple capture in a group pursuit problem with fractional derivatives”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S150–S157  mathnet  crossref  crossref  isi  elib
    10. N. N. Petrov, A. Ya. Narmanov, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v zadache prostogo presledovaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 193–198  mathnet  crossref  elib
    11. 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
    12. 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
    Citing articles in Google Scholar: Russian citations, English citations
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