Differential Game for an Infinite System of Two-Block Differential Equations

We present a pursuit differential game for an infinite system of two-block differential equations in Hilbert space l(2). The pursuer and evader control functions are subject to integral constraints. The differential game is said to be completed if the state of the system falls into the origin of l(2) at some finite time. The purpose of the pursuer is to bring the state of the controlled system to the origin of the space l(2), whereas the evader's aim is to prevent this. For the optimal pursuit time, we obtain an equation and construct the optimal strategies for the players.