Complete Solution of a Class of Differential Pursuit Games with Integral Constraint and Impulse Control

This article considers a class of differential games for which the problem of whether it is possible or impossible for the pursuer to catch the evader from a given initial point is finally solved using the method of resolving functions. An integral constraint is imposed on the controls of the pursuer, while the control of the evader is of impulse nature and is represented using a generalized Dirac function.