Some Results on Pursuit Games for an Infinite System of Ternary Differential Equations

Abstract

This paper aims to study a one-pursuer, one evader pursuit differential game for a higher level of infinite system that is an infinite system of first order ternary differential equations, and prove completion of pursuit in the game. Both integral constraints and geometric constraints are subjected on the players' control functions, thus two separate cases of pursuit games are examined. In the game, the pursuer wants to take the state of the system into the origin of l2 space at some finite time interval, whereas evader avoids this from happening. For every case, we solve the control problem by establishing the admissible control function. In order to achieve the pursuer's objective, we then construct an admissible strategy for the pursuer and develop an equation for the guaranteed pursuit time of the game.