Discrete Pursuit Game when Controls are subjected to Geometric and Total Constraints

We study two linear discrete game problems, where dynamics of pursuer and evader are described by two different type equations. The terminal set is a subset of R-n. In the first problem, controls of players are subjected to geometric constraints, and, in the second one, controls are subjected to total constraints. We obtain sufficient conditions of completion pursuit from certain initial positions of the players in finite time interval. Strategy of the pursuer is constructed based on information about initial positions of players and current value of the control parameter of the evader.