Abstract:
In a finite-dimensional Euclidean space, we consider a problem of pursuing one evader by a group of pursuers with equal capabilities of all participants. The dynamics of the problem is described by the system D(α)zi=azi+ui−v,ui,v∈V, where D(α)f is the Caputo derivative of order α∈(1,2) of the function f. The set of admissible controls V is a strictly convex compact set and a is a real number. The aim of the group of pursuers is to catch the evader by at least m different pursuers, possibly at different times. The terminal sets are the origin. The pursuers use quasi-strategies. We obtain sufficient conditions for the solvability of the pursuit problem in terms of the initial positions. The investigation is based on the method of resolving functions, which allows us to obtain sufficient conditions for the termination of the approach problem in some guaranteed time.
Keywords:
differential game, group pursuit, multiple capture, pursuer, evader.
Citation:
N. N. Petrov, “A multiple capture in a group pursuit problem with fractional derivatives”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 1, 2018, 156–164; Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S150–S157
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\paper A multiple capture in a group pursuit problem with fractional derivatives
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 1
\pages 156--164
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2019
\vol 305
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\pages S150--S157
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Linking options:
https://www.mathnet.ru/eng/timm1504
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This publication is cited in the following 7 articles:
A. I. Machtakova, “Lineinaya zadacha gruppovogo presledovaniya s drobnymi proizvodnymi i raznymi vozmozhnostyami igrokov”, Izv. IMI UdGU, 62 (2023), 43–55
N. N Petrov, A. I Machtakova, “Lineynaya zadacha gruppovogo presledovaniya s drobnymi proizvodnymi, prostymi matritsami i raznymi vozmozhnostyami igrokov”, Differentsialnye uravneniya, 59:7 (2023), 933
N. N. Petrov, A. I. Machtakova, “Linear Group Pursuit Problem with Fractional Derivatives, Simple Matrices, and Different Possibilities of Players”, Diff Equat, 59:7 (2023), 933
N. N. Petrov, “Multiple capture in a group pursuit problem with fractional derivatives and phase restrictions”, Mathematics, 9:11 (2021), 1171
M. Gomoyunov, “Solution to a zero-sum differential game with fractional dynamics via approximations”, Dyn. Games Appl., 10:2 (2020), 417–443
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
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