Synchronous implementation of simultaneous multiple captures of evaders

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.