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

Abstract

The present paper is devoted to studying a pursuit differential game described by an infinite system of binary differential equations in Hilbert space l2. 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 l2, 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.