Geodesic
On the capture of two evaders in a~non-stationary pursuit--evasion problem with phase restrictions
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 1, pp. 12-20

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We consider a linear problem of pursuing two evaders by a group of persecutors in case of equal dynamic opportunities of all participants and under phase restrictions imposed on the states of evaders. We assume that the evaders use the same control. The movement of each participant has the form $\dot z+a(t)z=w$. Geometric constraints on the control are strictly convex compact set with smooth boundary, and terminal sets are the origin of coordinates. It is assumed that the evaders do not leave the convex cone. The aim of a group of pursuers is to capture two evaders; the aim of a group of evaders is opposite. We say that a capture holds in the problem of pursuing two evaders if among the specified number of pursuers there are two of them who catch the evaders, possibly at different times. We obtain sufficient conditions for capturing two evaders in terms of initial positions. The results obtained are illustrated by examples.
Keywords: differential game, phase restrictions, piece-program strategy, counterstrategy. 
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     author = {M. N. Vinogradova},
     title = {On the capture of two evaders in a~non-stationary pursuit--evasion problem with phase restrictions},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {12--20},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2015_25_1_a1/}
}
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M. N. Vinogradova. On the capture of two evaders in a~non-stationary pursuit--evasion problem with phase restrictions. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 1, pp. 12-20. http://geodesic.mathdoc.fr/item/VUU_2015_25_1_a1/