An Approach for Solving Discrete Game Problems with Total Constraints on Controls

We consider a linear pursuit game of one pursuer and one evader whose motions are described by different‐type linear discrete systems. Controls of the players satisfy total constraints. Terminal set M is a subset of ℝn and it is assumed to have nonempty interior. Game is said to be completed if y(k) − x(k) ∈ M at some step k. To construct the control of the pursuer, at each step i, we use positions of the players from step 1 to step i and the value of the control parameter of the evader at the step i. We give sufficient conditions of completion of pursuit and construct the control for the pursuer in explicit form. This control forces the evader to expend some amount of his resources on a period consisting of finite steps. As a result, after several such periods the evader exhausted his energy and then pursuit will be completed.