On an approach to constructing the control of the first player in a single-type differential game with a ring-shaped terminal set

In a normed space of finite dimension we consider a single-type differential game. The vectograms of the players are described by the same ball with different time-dependent radii. The motion is constructed using polygonal lines. The terminal set is determined by the condition that the norm of the phase vector belongs to a segment with positive ends. In this paper, a set defined by this condition is called a ring. The aim of the first player is to lead a phase vector to the terminal set at fixed time. The aim of the second player is the opposite. In this paper, a new approach to constructing of the first player control is proposed. Unlike the previously obtained results, the construction of such a control does not require the calculating of the outer radius of the maximal stable bridge at each time moment, which is an undoubted advantage of the proposed approach from the point of view of computational procedures creating.