A Two-team Linear Quadratic Differential Game of Defending a Target

In this paper we consider the operational scenario where two missiles (attackers) are launched against a stationary target. Two interceptor missiles are fired in order to intercept the attackers. A non-homogeneous scenario is considered where the two attackers represent different levels of threat to the target and it it desired to be able to redirect an interceptor accordingly. The problem is posed as a Linear Quadratic Differential Game (LQDG) with several representative terminal weights and where the players also consider their energy expenditure. The closed-form solution to this zero-sum differential game which can be implemented in a state feedback form is provided in this paper. This type of solution is highly desirable in differential games since only by implementing closed-loop state feedback strategies the players are able to exploit non-optimal plays by the opponent and shift the Value of the game in their favor.