Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space l2

The present paper is devoted to studying a pursuit differential game described by an infinite system of binary differential equations in Hilbert space l 2 . The control parameters of the players are subject to geometric constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space l 2 , and oppositely, the evader tries to avoid it. Our aim is to construct a strategy for the pursuer to complete a differential game and an evasion control. We obtain an equation for the guaranteed pursuit and evasion times.