Pursuit in the Presence of a Defender

A zero-sum pursuit-evasion differential game with three players, a Target, an Attacker, and a Defender, is considered. The Attacker pursues the Target aircraft, while the Defender strives to intercept the Attacker before he reaches the aircraft. In this paper, the game in the state space region where the Attacker prevails is analyzed. The state space region where the Target is vulnerable is characterized and the Attacker's strategy for capturing the Target despite the presence of the Defender is derived. The players' optimal strategies mesh with the previously obtained strategies in the state space region where the Active Target Defense Differential Game is played, and the Defender's presence by virtue of him intercepting the Attacker allows the Target to escape.