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Home » Issues » Archive of Issues » 2017 - 3 issue » pp. 389-395

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Russia Izhevsk
Year
2017
Volume
27
Issue
3
Pages
389-395
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Section Mathematics
Title To a nonlinear pursuit problem with discrete control
Author(-s) Shchelchkov K.A.a
Affiliations Udmurt State Universitya
Abstract A two-person differential game is considered. The game is described by the following system of differential equations $\dot x = f(x, u) + g(x, v)$, where $x \in \mathbb R^k$, $u \in U$, $v \in V$. The pursuer's admissible control set is a finite subset of phase space. The evader's admissible control set is a compact subset of phase space. The pursuer's purpose is a translation of phase coordinates to zero. The evader's purpose is to prevent implementation of pursuer's purpose. Sufficient conditions on game parameters for the existence of zero neighborhood from which a capture occurs, that is translation of phase coordinates to zero, have been received. Also, it is proved that a period of time necessary for the pursuer to translate phase coordinates to zero tends to zero with the approaching of the initial position to zero. It happens regardless of the evader's control.
Keywords differential game, pursuer, evader, nonlinear system
UDC 517.977
MSC 49N70, 49N75
DOI 10.20537/vm170308
Received 26 June 2017
Language Russian
Citation Shchelchkov K.A. To a nonlinear pursuit problem with discrete control, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 3, pp. 389-395.
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