Geodesic
A nonlinear pursuit problem with discrete control and incomplete information
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 111-118 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 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 to capture the evader, viz. system translation to any given neighborhood of zero. Sufficient conditions for the solvability of a capture problem in the piecewise open-loop strategies class are obtained. In addition, it is proved that the capture time tends to zero with the initial position approaching to zero. It happens independent of the evader's actions.
Keywords: differential game, pursuer, evader, nonlinear system. 
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K. A. Shchelchkov. A nonlinear pursuit problem with discrete control and incomplete information. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 111-118. http://geodesic.mathdoc.fr/item/VUU_2018_28_1_a9/

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