We consider a pursuit-evasion differential game problem in which countably many pursuers chase one evader in the Hilbert space ${\ell_2}$ and for a fixed period of time. Dynamic of each of the pursuer is governed by first order differential equations and that of the evader by a second order differential equation. The control function for each of the player satisfies an integral constraint. The distance between the evader and the closest pursuer at the stoppage time of the game is the payoff of the game. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. We constructed optimal strategies of the players and find value of the game.

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关于希尔伯特空间中追逃逃逸的差分博弈问题

我们考虑了追逃逃避的差分博弈问题，在该问题中，无数追赶者在希尔伯特空间$ {\ ell_2} $中追逐一个逃避者，并保持固定的时间。每个追踪器的动力由一阶微分方程控制，而逃逸者的动力由二阶微分方程控制。每个玩家的控制功能都满足积分约束。在游戏停止时逃避者和最接近的追随者之间的距离是游戏的收益。追击者的目标是使到逃避者的距离最小化，而逃避者的距离则相反。我们构建了玩家的最佳策略并找到了游戏的价值。