Abstract:
In the finite-dimensional Euclidean space, the problem of a group of pursuers pursuing a group of evaders is considered, which is described by the system ˙zij=ui−vj,ui,vj∈V.˙zij=ui−vj,ui,vj∈V. The set of admissible controls is a convex compact, and the target's sets are the origin of coordinates. The aim of the group of pursuers is to carry out an rr-fold capture of at least qq evaders. Additionally, it is assumed that the evaders use program strategies and that each pursuer can catch no more than one evader. We obtain necessary and sufficient conditions for the solvability of the pursuit problem. For the proof we use the Hall theorem on the system of various representatives.
Keywords:
differential game, group pursuit, pursuer, evader.
Citation:
N. N. Petrov, A. Ya. Narmanov, “Multiple capture of a given number of evaders in the problem of a simple pursuit”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:2 (2018), 193–198
\Bibitem{PetNar18}
\by N.~N.~Petrov, A.~Ya.~Narmanov
\paper Multiple capture of a given number of evaders in the problem of a simple pursuit
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 2
\pages 193--198
\mathnet{http://mi.mathnet.ru/vuu630}
\crossref{https://doi.org/10.20537/vm180205}
\elib{https://elibrary.ru/item.asp?id=35258686}
Linking options:
https://www.mathnet.ru/eng/vuu630
https://www.mathnet.ru/eng/vuu/v28/i2/p193
This publication is cited in the following 13 articles:
N. N. Petrov, N. A. Solov'eva, “Multiple Capture of a Given Number of Evaders in L. S. Pontryagin's Recurrent Example”, J Math Sci, 2024
A. I. Blagodatskikh, “Sinkhronnaya realizatsiya odnovremennykh mnogokratnykh poimok ubegayuschikh”, Izv. IMI UdGU, 61 (2023), 3–26
B. T. Samatov, U. B. Soyibboev, “Differential game with “lifeline” for Pontryagin's control example”, Izv. IMI UdGU, 61 (2023), 94–113
N. N. Petrov, “Dvukratnaya poimka skoordinirovannykh ubegayuschikh v zadache prostogo presledovaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:2 (2023), 281–292
A. I. Blagodatskikh, A. S. Bannikov, “Odnovremennaya mnogokratnaya poimka pri nalichii zaschitnikov ubegayuschego”, Izv. IMI UdGU, 62 (2023), 10–29
Nikolay N. Petrov, “On the Problem of Pursuing Two Coordinated Evaders in Linear Recurrent Differential Games”, J Optim Theory Appl, 197:3 (2023), 1011
N. N. Petrov, N. A. Solov'eva, “Problem of multiple capture of given number of evaders in recurrent differential games”, Sib. elektron. matem. izv., 19:1 (2022), 371–377
N. N. Petrov, “Ob odnoi zadache prostogo presledovaniya dvukh zhestko skoordinirovannykh ubegayuschikh”, Izv. IMI UdGU, 59 (2022), 55–66
B. T. Samatov, A. Kh. Akbarov, B. I. Zhuraev, “Pursuit–evasion differential games with Gr-constraints on controls”, Izv. IMI UdGU, 59 (2022), 67–84
V. I. Ukhobotov, V. N. Ushakov, “Ob odnoi zadache upravleniya s pomekhoi i vektogrammami, zavisyaschimi lineino ot zadannykh mnozhestv”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:3 (2020), 429–443
N. N. Petrov, N. A. Soloveva, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v rekurrentnom primere L. S. Pontryagina”, Materialy Vserossiiskoi nauchnoi konferentsii «Differentsialnye uravneniya i ikh prilozheniya», posvyaschennoi 85-letiyu professora M. T. Terekhina. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 17–18 maya 2019 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 186, VINITI RAN, M., 2020, 108–115
N. N. Petrov, A. I. Machtakova, “Poimka dvukh skoordinirovannykh ubegayuschikh v zadache s drobnymi proizvodnymi, fazovymi ogranicheniyami i prostoi matritsei”, Izv. IMI UdGU, 56 (2020), 50–62
N. N. Petrov, A. Ya. Narmanov, “Multiple Capture of a Given Number of Evaders in a Problem with Fractional Derivatives and a Simple Matrix”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S105–S115
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