The method of resolving functions for solving a pursuit problem with integral constraints on player controls

In this paper, we study pursuit game problems described by a system of equations with a retarded argument under integral constraints on the players' controls. The proposed scheme uses the ideas of the method of resolving functions. Modifications of methods (i.e., the first and so-called third methods) [1,3,12] of pursuit are proposed in the case when integral constraints are imposed on the players' controls. Sufficient conditions are obtained for the possibility of completing the pursuit in a finite time.