Pursuit game problem of an infinite system of differential equations with geometric and integral constraints

The present paper considers a pursuit game problem of an infinite system of 1st-order differential equations in the space l(2). In the game, the player's control functions satisfy both geometric and integral constraints. The pursuer's action is to force the state of the system to coincides with another state for a finite time and the evader's action is to retrieve this. In each case, we obtain a condition for the completion of the game for which the pursuer's strategy is explicitly constructed. In addition, we study a control problem.