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This article is cited in 1 scientific paper (total in 1 paper)
MATHEMATICS
To a nonlinear pursuit problem with discrete control
K. A. Shchelchkov Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
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.
Received: 26.06.2017
Citation:
K. A. Shchelchkov, “To a nonlinear pursuit problem with discrete control”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017), 389–395
Linking options:
https://www.mathnet.ru/eng/vuu596 https://www.mathnet.ru/eng/vuu/v27/i3/p389
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