Pursuit Problem of Low-Maneuverable Objects with a Ring-Shape Terminal Set

In this paper, we consider a pursuit problem for two moving objects, a pursuer and an evader. The objects move in the same plane under the influence of controlled forces directed always perpendicular to their velocities. The laws of variation of these forces are determined by first-order controllers. The capture is determined by the condition that the relative distance between the objects belongs to a segment with positive endpoints. For the problem considered, we construct a control of the pursuer that guarantees the catch.