A differential game with two pursuers and one evader

Abstract

This paper is concerned with a coplanar pursuit-evasion problem in which a faster evaderE with constant speedw>1 must pass between two pursuersP ₁,P ₂ having unit speed, the payoff being the distance of closest approach to either one of the pursuers. The control variables are the directions of the velocities ofP ₁,P ₂, andE. The path equations are integrated, and a closed-form solution is obtained in terms of elliptic functions of the first and second kind. A closed-loop solution is given graphically in several diagrams, for different values ofw.