Optimal Pursuit Differential Game Problem for an Infinite System of Binary Differential Equations

We study a differential game problem for an infinite system of binary differential equations. The control functions of pursuer and evader are subjected to integral constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space \(l_{2}\) and the aim of the evader is opposite. An equation for the optimal pursuit time is obtained and optimal controls of players are constructed. Also, an auxiliary optimal control problem is solved to prove the main result of the paper.