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Home » Issues » Archive of Issues » 2023 - 1 issue » pp. 130-140

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Russia Izhevsk
Year
2023
Volume
33
Issue
1
Pages
130-140
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Section Mathematics
Title On a group pursuit problem on time scales
Author(-s) Mozhegova E.S.a
Affiliations Udmurt State Universitya
Abstract In a finite-dimensional Euclidean space $\mathbb R^k$, we consider a linear problem of pursuit of one evader by a group of pursuers, which is described on the given time scale $\mathbb{T}$ by equations of the form \begin{gather*} z_i^{\Delta} = a z_i + u_i - v, \end{gather*} where $z_i^{\Delta}$ is the $\Delta$-derivative of the functions $z_i$ on the time scale $\mathbb{T}$, $a$ is an arbitrary number not equal to zero. The set of admissible controls for each participant is a unit ball centered at the origin, the terminal sets are given convex compact sets in $\mathbb R^k$. The pursuers act according to the counter-strategies based on the information about the initial positions and the evader control history. In terms of initial positions and game parameters, a sufficient capture condition has been obtained. For the case of setting the time scale in the form $\mathbb T = \{ \tau k \mid k \in \mathbb Z,\ \tau \in \mathbb R,\ \tau >0\}$ sufficient pursuit and evasion problems solvability conditions have been found. In the study, in both cases, the resolving function method is used as basic one.
Keywords differential game, group pursuit, pursuer, evader, time scale
UDC 517.977
MSC 49N79, 49N70, 91A24
DOI 10.35634/vm230109
Received 21 December 2022
Language Russian
Citation Mozhegova E.S. On a group pursuit problem on time scales, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 1, pp. 130-140.
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