An application of the epsilon technique to the solution of pursuit and evasion problems

Abstract

A necessary and sufficient condition for attaining capture in pursuit and evasion problems described by nonlinear differential equations are presented. It is shown that the “epsilon technique” developed by A. V. Balakrishnan for computing optimal control can be applied for solving the pursuit and evasion problems. The existence of the solution for the epsilon problem is proved, and the relation between the original pursuit problem and the epsilon problem is shown.