Synchronous implementation of simultaneous multiple captures of evaders

A. I. Blagodatskikh
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Abstract

The problem of pursuit of a group of $m$ evaders $(m\geqslant 1)$ in conflict-controlled processes with equal opportunities is considered. It is said that in the problem of chasing one evader $(m = 1)$, multiple capture occurs if a given number of pursuers catch him, and the moments of capture may not coincide. In the problem of simultaneous multiple capture of one evader, it is required that the moments of capture coincide. Simultaneous multiple capture of the whole group of evaders $(m \geqslant 2)$ occurs if, as a result of pursuit, each evader is repeatedly caught simultaneously, and at the same time. In terms of the initial positions of the participants, necessary and sufficient conditions for the simultaneous multiple capture of the whole group of evaders are obtained.
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同时捕获多个逃税者的同步实现
研究了机会均等的冲突控制过程中$m$逃逃者$(m\geqslant 1)$群体的追捕问题。据说,在追捕一个逃逃者$(m = 1)$的问题中,如果给定数量的追捕者抓住了他,则会发生多次捕获,并且捕获的时刻可能不一致。在同时捕获多个逃兵的问题中,要求捕获的力矩一致。如果在追捕过程中,每个逃兵在同一时间同时被多次捕获,则整个逃兵群体$(m \geqslant 2)$会同时被多次捕获。根据参与者的初始位置,得到了同时多次捕获整个逃逃者群的充分必要条件。
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