The Target Differential Game with Two Defenders

A cooperative aircraft differential game where an Attacker missile pursues an unmanned aerial vehicle (UAV) herein called the Target is addressed. The Target UAV cooperates with up to two Defender missiles which are launched in order to intercept the Attacker before the latter reaches the Target. This is a scenario with important military applications where each one of the agents is an autonomous air vehicle. Each agent plans and corrects its course of action in order to defeat an opposing force while simultaneously optimizing an operational relevant cost/payoff performance measure. The Target and the Defenders cooperate to form a team against the Attacker. The results in this paper build on the solution of a three agent differential game, where the three players are the Target, the Attacker, and one Defender; in this paper, the benefits of firing a second Defender are considered. Indeed, launching two interceptor missiles is a standard procedure by providing redundant backup. Building on the solution of the one-Defender problem, it is possible to address a seemingly intractable problem, where the Target needs to decide which Defender(s) to cooperate with, in addition to obtaining the optimal headings of every player in the game. Given the initial positions of the players, we solve the problem of determining if a second Defender improves the Target/Defender(s) payoff and provide the optimal strategies for each of the agents involved. Finally, we address the game of kind (for the case of one Defender) which provides the safety regions to determine which side will win based on the initial state. These safety regions provides the Target’s area of vulnerability, and using these results, we describe the reduction to the Target’s vulnerability area brought by an additional Defender.