Optimal Strategies for the Target-Attacker-Defender Differential Game in 3D Space

A differential game is discussed with three players in three dimensions: a target, a defender and an attacker, in which the attacker attempts to capture the target while the target attempts to move away from the attacker. Additionally, the defender’s goal is to capture the attacker before the attacker reaches the target. This paper provides a solution to the differential game in a three-dimensional state space, consider that the attacker plays two roles: it has to capture the target and evade the defender at the same time. Therefore we design a composite payoff function that takes into account both the attacker-target distance and the attacker-defender distance. We address the optimal feedback strategies for three players with different weight coefficients. We provide the optimal trajectory for the players of the Target-Attacker-Defender differential game under different initial conditions through simulation experiments and analyze the influence of different parameters on the outcome of the game.