Abstract:
In a finite-dimensional Euclidean space, the pursuing problem of a group of evaders by a group of pursuers with equal
opportunities for all participants is considered.
The movement of each participant is described by a linear system of differential equations with a simple matrix.
The set of admissible controls for each player is a ball of unit radius with a center at the origin.
The target set is the origin.
It is assumed that all evaders use the same control and each evader does not leave the boundaries of a convex
polyhedral set with a nonempty interior.
It is proved that if the number of pursuers is less than the dimension of the space, then all evaders evade capture.
Keywords:differential game, group pursuit, pursuer, evader, phase restrictions.
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