Comparison of the solutions of linear and non-linear positional differential games of encounter

Abstract

A positional differential game of encounter of a non-linear, conflict-controlled system with a given target set is considered. Sufficient conditions for a successful encounter of the initial system with the target set are given. The differential game problem of encounter between two objects with restricted manoeuvrability is solved. The equations of motion of the objects and the constraints imposed on the controls are given using the same relations as those in the differential game known /1/ as the “two-car game”. It is assumed that both objects have restricted manoeuvrability and the game takes place over a fixed time interval. A positional strategy is constructed for the pursuer guaranteeing that it arrives at a previously specified distance from the pursued at the instant of game termination. The paper is related to work done in /1–14/.