On the problem of group pursuit

This paper is devoted to an investigation of the problem of pursuit of a single evader by a group of pursuers. Sufficient conditions are presented for the existence of a solution of it, the properties of this solution are described, and a method is presented for constructing pursuer controls that solve the problem. The method is based on the idea of the first direct method of Pontryagin, which has had a large influence on the development of many parts of the theory of differential games.