Integral Constraints Pursuit Problem for 3 System of Differential Equations in Hilbert space

Abstract

This paper investigates a pursuit game of an infinite 3-system of differential equations involving one pursuer and one evader. Integral constraints are imposed on the players’ control parameters where the resource of the pursuer is greater than that of the evader. The aim of the pursuer is to bring the initial state 0 of the system into another non-zero state 1 of the system at some timeon a finite time interval to complete the pursuit. We constructed a control function needed in solving control problems of the system and developed an admissible pursuer’s strategy to solve the pursuit problem. Pursuit is shown to be completed in the game as the state of the system reaches state 1 at afinite time >0.