Active target defense differential game

A pursuit-evasion differential game involving three agents is discussed. This scenario considers an Attacker missile pursuing a Target aircraft. The Target is however aided by a Defender missile launched by, say, its 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 distance between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, and the Attacker which tries to minimize said distance. The solution to this differential game provides optimal heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker and it also provides the optimal heading angle for the Attacker to minimize the said distance.