New strategies for some pursuit-evasion differential games with Gronwall-type constraints

Abstract

This paper studies a class of non-cooperative pursuit-evasion differential games in the sequence space $l_{2}.$ The motions of the pursuer and the evader are described by certain first-order differential equations while their control functions are subject to Gronwall-type constraints which impose history-dependent bounds on their control resources. Two fundamental problems are investigated. For the pursuit problem, new strategy for the pursuer is constructed and sufficient conditions guaranteeing the completion of pursuit are established. For evasion problem, an admissible strategy of the evader ensuring avoidance of capture is obtained, and corresponding sufficient conditions for successful evasion are derived. The proposed approached extends existing results on differential games with classical geometric and integral constraints to a broader class of systems governed by Gronwall-type restrictions.