A game theoretic approach — evasion problem for a linear system with integral constraints imposed on the player control

Abstract

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 in /1, 2/ 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 /3/ 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 in /4/. 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. The present paper is related to the investigations described in /1–8/.