On continuous strategies of deviation from a nonconvex set under uncertainty conditions

Abstract

Studies are made of continuous methods of the deviation in one differential game on the plane with a nonconvex terminal set. The game is nondegenerate in the sense that the programmed controls give no way of affording the deviation and there exists a (discontinuous) method of feedback control that guarantees the deviation. The problem under study can serve as an example of the nondegenerate differential game with a nonconvex terminal set, in which the attempt fails to assure the deviation with the aid of feedback control methods described by continuous mappings. Strategies are investigated that satisfy the Caratheodory conditions and contain the argument deviation. Despite the nonconvexity of the terminal set, by which the circumference serves, it is possible to perform the proof of the unsolvability with the aid of a rather simple mathematical technique on the basis of the Schauder theorem for the fixed point.