On Game Problems of Controlling Pencil Trajectories under Integral Constraints on the Controls of Players

The game problems of control of pencil trajectories, described by a system of equations with a retarded argument under integral restrictions on the players’ controls, are studied. Modifications of the first (I) and third (III) pursuit methods are proposed for game problems of control pencil trajectories. For this game, sufficient conditions are obtained for the possibility of transferring pencil trajectories.