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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 2, Pages 178–186 (Mi timm1180)  

This article is cited in 6 scientific papers (total in 6 papers)

Multiple capture in Pontryagin's recursive example with phase constraints

N. N. Petrov, N. A. Solov'eva

Udmurt State University, Mathematical Department

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.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, 293, suppl. 1, 174–182

Bibliographic databases:

UDC: 517.977
Received: 10.02.2015

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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\paper Multiple capture in Pontryagin's recursive example with phase constraints
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 2
\pages 178--186
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 293
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\pages 174--182
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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. 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
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
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