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Guaranteed pursuit time in a differential game with coordinate-wise integral constraints

The present paper proposes differential game of pursuit described by system of infinite first order ordinary differential equations. The game focuses only on one-pursuer and one-evader differential game and the coordinate wise integral constraints are imposed on the player’s control functions. The pursuit is assumed to be completed if the pursuer brings the state of the system from one state in to another state at some time. We proved a theorem on a guaranteed pursuit time. Moreover, an explicit strategy of pursuer is constructed.