Guaranteed Pursuit Time for an Infinite System in $l_2$ with Geometric Constraints

In this paper, we consider a pursuit differential game problem described by an infinite system of binary differential equations in the Hilbert space l2. The control parameters of the players are subject to geometric constraints. The pursuer's goal is to complete the game by bringing the state of the system to the origin, while the evader's goal is the contrary. The guaranteed pursuit time required to achieve the pursuer's goal is estimated. To this end, we constructedan optimal strategy for the pursuer.