Guaranteed result in solving the game problems of motion control

The paper is devoted to investigation of the nonstationary games of approach. The goal of this study is to clarify how the availability of information on the evader's control prehistory to the pursuer affects value of a fixed guaranteed time of the game termination. The issue is explored on the basis of the Method of Resolving Functions, providing sufficient conditions for approach. Governing set-valued mapping is constructed, ensuring guaranteed result without knowledge of the evader's control prehistory. Also condition is deduced which provides for the mapping to be convex-valued. Significance of this condition is illustrated with the "simple motions" example.