Open-loop solution of a defender-attacker-target game: penalty function approach

A defender-attacker-target problem with non-moving target is considered. This problem is modelled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional. In this game, the pursuer is the defender, while the evader is the attacker. The objective of the pursuer is to minimise the cost functional, while the evader has two objectives: to maximise the cost functional and to keep a given terminal state inequality constraint. The open-loop saddle point solution of this game is obtained in the case where the transfer functions of the controllers for the defender and the attacker are of arbitrary orders.