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

Abstract

We study an optimal pursuit differential game problem in the Hilbert space $$l_{r+1}^2$$ . The game is described by an infinite system of the first-order differential equations whose coefficients are negative. The control functions of players are subjected to integral constraints. If the state of the system coincides with the origin of the space $$l_{r+1}^2$$ , then game is considered completed. We obtain an equation to find the optimal pursuit time. Moreover, we construct the optimal strategies for players.