Extremal strategies in differential games with integral constraints: PMM vol. 36, n≗1, 1972, pp. 15–23

Abstract

The game problem is considered of taking a controlled motion onto a given set. It is assumed that the players' controls are subject to integral constraints. The first player's extremal strategy is described, forming a feedback control. It is shown that under the conditions of absorption stability the extremal strategy guarantees the termination of the pursuit at the instant of program absorption. A modification is suggested of the extremal strategies, described in [1, 2], in differential games with constraints on the instantaneous values of the players' controls. This paper is closely related to [2–6].