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Control strategies for multiplayer target-attacker-defender differential games with double integrator dynamics

机译：具有双重积分动态的多人目标-防御者-差分游戏的控制策略

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摘要

This paper presents a method for deriving optimal controls and assigning attacker-defender pairs in a target-attacker-defender differential game between an arbitrary numbers of attackers and defenders, all of which are modeled using double integrator dynamics. It is assumed that each player has perfect information about the states and controls of the players within a certain range of themselves, but they are unaware of any players outside of this range. Isochrones are created based on the time-optimal trajectories needed for the players to reach any point in the shortest possible time. The intersections of the players' isochrones are used to determine whether a defender can intercept an attacker before the attacker reaches the target. Sufficient conditions on the detection range of the defenders and the guaranteed capture despite perturbations of the attackers off the nominal trajectories are derived. Then, in simulations with multiple players, attacker-defender pairs are assigned so that the maximum number of attackers are intercepted in the shortest possible time.
机译：本文提出了一种方法，用于在任意数量的攻击者和防御者之间的目标—攻击者—防御者差分博弈中派生最佳控制并分配攻击者—防御者对，所有这些都使用双积分器动力学建模。假定每个玩家在自己的一定范围内都具有关于玩家的状态和控制的完美信息，但是他们不知道该范围之外的任何玩家。等时线是根据玩家在最短时间内到达任意点所需的最佳时间轨迹创建的。玩家等时线的交点用于确定防御者在攻击者到达目标之前是否可以拦截攻击者。得出了尽管攻击者偏离了名义轨迹的干扰，但防御者的探测距离和保证的俘获的充分条件。然后，在具有多个玩家的模拟中，分配了攻击者-防御者对，以便在尽可能短的时间内拦截最大数量的攻击者。

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