Linear Discrete Pursuit Game with Phase Constraints

الملخص EN

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.