Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

Abstract

In this paper we study a linear pursuit differential game described by an infinite system of first-order differential equations in Hilbert space. The control functions of players are subject to geometric constraints. The pursuer attempts to bring the system from a given initial state to the origin for a finite time and the evader's purpose is opposite. We obtain a guaranteed pursuit time and construct a strategy for pursuer.