A game theoretic approach-evasion problem for a linear system with integral constraints imposed on the player control
A differential approach-evasion game with integral constraints imposed on the player controls is considered. A positional strategy is proposed, supplying a solution to the approach problem, and conditions are given under which the set of programmed absorption has the property of stability. Differential games of this type were first studied by \textit{N. N. Krasovskij} [''Theory of motion control. Linear systems'' (1968; Zbl 0172.127)] and by \textit{N. N. Krasovskij} and \textit{V. E. Tret'yakov} [Sov. Phys., Dokl. 12, 205-207 (1967; Zbl 0212.481)], where the pursuit- evasion problem was considered for single type systems, and auxiliary constructions were proposed for use as a basis in constructing a positional strategy in the form of the strategies of external aiming. Stable bridges of programmed absorption [see \textit{V. N. Ushakov}, J. Appl. Math. Mech. 36, 12-19 (1972; Zbl 0254.90078)] for linear, generally speaking, non-single type objects, were considered, and the construction of strategies extremal with respect to these bridges were demonstrated. A solution of the problem of approach in the class of positional procedures of control with a guide was proposed by \textit{A. I. Subbotin} and \textit{V. N. Ushakov} [ibid. 39, 367-375 (1976; Zbl 0363.90135)]. It should be noted that the question of whether it is possible to construct resolving positional strategies in differential games with integral constraints, remains open.
scientific article; zbMATH DE number 3920259