A pursuit problem described by infinite system of differential equations with coordinate-wise integral constraints on control functions

We consider a pursuit differential game of one pursuer and one evader described by infinite system of first order differential equations. The coordinate-wise integral constraints are imposed on control functions of players. By definition pursuit is said to be completed if the state of system equals zero at some time. A sufficient condition of completion of pursuit is obtained. Strategy for the pursuer is constructed and an explicit formula for the guaranteed pursuit time is given