Singular analysis of a multi-agent, turn-constrained, defensive game

摘要

We examine a two-team, differential game, which models an active target defense scenario. One team represents an attacking force and consists of a single Attacker. The opposing team represents a defensive force consisting of a high-value Target and a mobile Defender. The Attacker strives to get as close to the Target as possible before it is intercepted by the Defender. Conversely, the defensive team attempts to maneuver so that the Defender intercepts the Attacker as far from the Target as possible. The Attacker and Target move with simple motion, while the Defender has a constrained turn rate. We discuss two types of singular surfaces that appear within the equilibrium solution of this game, namely the universal surface and the dispersal surface. Several numerical examples are presented to illustrate the characteristics of the equilibrium solutions that interact with these surfaces.