On the Interrelation of Two Linear NonStationary Problems with Multiple Evaders

A linear nonstationary pursuit problem in which a group of pursuers and a group of evaders are involved is considered under the condition that the group of pursuers includes participants whose admissible controls set coincides with that of the evaders and participants whose admissible controls sets belong to interior of admissible controls set of the evaders. The aim of the group of pursuers is to capture all the evaders. The aim of the group of evaders is to prevent the capture, that is, to allow at least one of the evaders to avoid the rendezvous. It is shown that, if in the game in which all the participants have equal capabilities at least one of the evaders avoids the rendezvous on an infinite time interval, then as a result of the addition of any number of pursuers with less capabilities, at least one of the evaders will avoid the rendezvous on any finite time interval.