Defending an Asset with Partial Information and Selected Observations: A Differential Game Framework

This paper considers a linear-quadratic-Gaussian asset defending differential game (DADG) where the attacker and the defender do not know each other's state information. However, they both know the trajectory of a moving asset. Both players can choose to observe the other player's state information by paying a cost. The defender and the attacker have to craft both control strategies and observation strategies. We obtain a closed-form feedback solution that characterizes the Nash control strategies. We show that the trajectory of the asset does not affect both players' observation choices. Moreover, we show that we can decouple the observation choices of the defender and the attacker. One can obtain the Nash observation strategies by solving two independent optimization problems. A set of necessary conditions is developed to characterize the optimal observation instances. Based on the necessary conditions, we propose an effective algorithm to compute the optimal observation instances numerically. We also present a case study to demonstrate the effectiveness of the optimal observation instances.