Optimal Target Capture Strategies in the Target-Attacker-Defender Differential Game

A zero-sum differential game with three players, a Target, an Attacker, and a Defender is considered. The Attacker pursues the Target aircraft. The Defender strives to intercept the Attacker before it reaches the aircraft. The two termination set differential game is analyzed in this paper. The players' optimal state feedback strategies for the case where the Attacker is able to capture the Target despite the presence of the Defender are derived. It is also shown how these results mesh with the previously obtained strategies of active target defense in order to obtain the complete solution of this two termination set differential game.