A variant of the program iteration method called stability iterations is used for a differential game of pursuit–evasion. The successful solvability set of one of the problems generating the game is found as a limit of the iterative procedure in the space of sets whose elements are positions of the game. The game is defined by a pair of closed sets, one of the which is the target set in the pursuit problem (the first player’s problem) and the other specifies the state constraints in this problem. For the positions not belonging to the solvability set of the pursuit problem, it is interesting to determine the smallest “size” of a neighborhood of the two mentioned sets for which the first player can implement the guidance to the neighborhood of the target set corresponding to this “size” within the similar neighborhood of the second set, i.e., the set specifying the state constraints. Similar constructions are considered for the sets realized at each stage of the iterative procedure. We use the connection of these constructions with the mentioned smallest “size” of neighborhoods of the sets that are parameters of the differential game in the sense of guaranteed realizability of guidance under the replacement of the original sets by these neighborhoods.

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追求-逃避微分博弈的松弛和迭代方法

称为稳定性迭代的程序迭代方法的一种变体用于追赶-逃避的差分游戏。发现产生游戏的问题之一的成功可解性集是在其元素是游戏位置的集的空间中迭代过程的限制。游戏是由一对封闭的集合定义的，其中一个是追逐问题（第一个玩家的问题）中的目标集合，另一个是指定此问题中的状态约束。对于不属于追踪问题的可解性集合的位置，确定两个提到的集合的邻域的最小“大小”是有趣的，第一玩家可以针对该最小的“大小”实施对目标集合的邻域的指导。第二组相似邻域内的“大小”，即 指定状态约束的集合。对于在迭代过程的每个阶段实现的集合，考虑类似的构造。我们将这些构造与集合的邻域中提到的最小“大小”联系起来，这些最小邻域是差分博弈的参数，从这些邻域替换原始集合的角度出发，可以确保实现指导的意义。