Escape Regions of the Active Target Defense Differential Game

TL;DR

This paper analyzes a differential game involving an attacker missile, a target aircraft, and a defender missile, characterizing the initial conditions guaranteeing the target's survival under optimal strategies.

Contribution

It introduces a characterization of the escape regions in the active target defense differential game and derives the optimal strategies for all players.

Findings

Defined the set of initial positions ensuring target survival.

Derived optimal pursuit and evasion strategies.

Provided analytical solutions for the escape regions.

Abstract

The active target defense differential game is addressed in this paper. In this differential game an Attacker missile pursues a Target aircraft. The aircraft is however aided by a Defender missile launched by, say, the wingman, to intercept the Attacker before it reaches the Target aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the separation between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while the Attacker simultaneously tries to minimize said distance. This paper focuses on characterizing the set of coordinates such that if the Target's initial position belong to this set then its survival is guaranteed if both the Target and the Defender follow their optimal strategies. Such optimal strategies are presented in this paper as well.