Geodesic
To a nonlinear pursuit problem with discrete control
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 389-395 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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K. A. Shchelchkov. To a nonlinear pursuit problem with discrete control. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 389-395. http://geodesic.mathdoc.fr/item/VUU_2017_27_3_a7/

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