We study a pursuit differential game of many pursuers and one evader in the plane. We are given a compact convex subset of \({\mathbb {R}}^2\), and the pursuers and evader move in this set. They cannot leave this set during the game. Control functions of players are subject to coordinate-wise integral constraints. If the state of a pursuer coincides with that of evader at some time, then we say that pursuit is completed. Pursuers try to complete the pursuit, and the aim of the evader is opposite. We obtain some conditions under which pursuit can be completed from any positions of the players in the given set. Moreover, we construct strategies for the pursuers. Also, we prove some properties of convex sets.

中文翻译：

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紧凸集上具有积分约束的许多追求者的求异博弈

我们研究了飞机上许多追击者和一个躲避者的追逐差分游戏。我们得到了\（{\ mathbb {R}} ^ 2 \）的紧凸子集，追踪者和躲避者在该集合中移动。他们不能在比赛中离开这个场景。游戏者的控制功能受到坐标积分约束的约束。如果追踪者的状态有时与逃避者的状态一致，那么我们就说追踪已经完成。追求者试图完成追求，而逃避者的目标则相反。我们获得一些条件，在该条件下，可以从给定集合中的任何位置的玩家完成追逐。此外，我们为追求者制定策略。此外，我们证明了凸集的一些性质。