Abstract
A pursuit game of a stationary linear system with time-delay is considered here. The state of this system is infinite dimensional but the target set is finite dimensional. The mathematical model of the system is formulated here as a coupling of a lumped parameter subsystem and a distributed parameter subsystem, and the target set is defined as a subset in the state space of the lumped parameter subsystem.
In this pursuit game three different types of information patterns are defined. They are, respectively, (i) the open loop information pattern for the pursuer, (ii) the closed loop information pattern for the pursuer and (iii) the open loop information pattern for the evader. In (i) and (ii), one of the sufficient conditions for completion of the game and the pursuer's closed loop control are obtained. This pursuer's closed loop control u is constructed by the state x(t) of the lumped parameter subsystem, his opponent's control v(t) and the histories of x, u and v. It is shown that, in (iii), the evader can choose his feedback control for the game not to be completed in some finite time.
