Linear Quadratic Formulation of the Target Defense Differential Game

In this paper we revisit the Target Defense Differential Game and recast it as a linear quadratic differential game. In this game there are two players, a Defender and an Attacker; the target is stationary. The Attacker aims at the target trying to avoid the Defender while the Defender protects the target by blocking the Attacker's path to the target and trying to intercept the Attacker as far as possible from the target. The Attacker strives to minimize his distance from the Target at the moment of interception by the Defender. Each player is mindful of its energy expenditure by imposing appropriate quadratic weights on its control inputs. The analytical solution of this linear quadratic differential game is obtained in this paper which can be implemented in closed-loop form to provide robustness against non-optimal maneuvers by the opponent.