We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Position of the evader satisfies phase constraints: y ∈ G, where G is a subset of R n. We considered two cases: (1) controls of the players satisfy geometric constraints, and (2) controls of the players satisfy total constraints. Terminal set M is a subset of R n and it is assumed to have a nonempty interior. Game is said to be completed if y(k) − x(k) ∈ M at some step k; thus, the evader has not the right to leave set G. To construct the control of the pursuer, at each step i, we use the value of the control parameter of the evader at the step i. We obtain sufficient conditions of completion of pursuit from certain initial positions of the players in finite time interval and construct a control for the pursuer in explicit form.
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机译：我们考虑一个由一个追随者和一个逃避者组成的线性追逐游戏，其运动由不同类型的线性离散系统描述。逃避器的位置满足相位约束：y∈G，其中G是R n 的子集。我们考虑了两种情况：（1）玩家的控件满足几何约束，并且（2）玩家的控件满足总约束。终端机M是R n 的子集，并且假定其内部为非空。如果在某个步骤k处y（k）-x（k）∈M，则游戏结束。因此，逃避者没有离开集合G的权利。为了构造对追随者的控制，在每个步骤i中，我们在步骤 i 中使用逃避者的控制参数的值。我们在有限的时间间隔内从玩家的某些初始位置获得了足够的追踪完成条件，并以显式形式构造了追踪者的控件。
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