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

Abstract

We present a pursuit differential game for an infinite system of two-block differential equations in Hilbert space l2. 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 l2 at some finite time. The purpose of the pursuer is to bring the state of the controlled system to the origin of the space l2, 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.

On a linear differential game in the Hilbert space $\ell^2$

“…Differential games for infinite dimensional systems are also well studied, for example, when the evolution of the system is governed by parabolic equations pursuit evasion problems are considered in [21][22][23], where the problem for the partial differential equations is reduced to an infinite system of ordinary differential equations. Pursuit evasion games with many players considered in [3,[17][18][19]23].…”

Preface to the Special Issue on “Differential Games and Its Applications”

“…Ibragimov et al [8] show a chase differential game for an infinite system of two-block differential equations in the Hilbert space l 2 . The control functions for both the pursuer and the evader are bound by integral restrictions.…”