To the Theory of Many-Person Differential Games

A linear differential game of a group of pursuers and one evader is considered. Sufficient conditions for the solvability of a problem of pursuit are presented in the case when it is possible to split pursuers into the following three groups of players. For the players of the first, second, and third groups, the dynamic capabilities, respectively, coincide with, exceed, and are less than the dynamic capabilities of the evader. An algorithm for finding a control of pursuing players is described. A method for calculating the guaranteed time of visiting the terminal set from a given initial position is proposed. The results of calculation of a model example are presented.