A Stochastic Differential Game with Controllable Statistical Parameters

A differential game is described where the opponents are a missile and a radar. The problem is formulated so that linear theory can be used in finding the optimal strategies of both opponents. The missile uses a mixed strategy by adding white noise into its controller. The statistics of this noise (the covariance completely describes the noise) can be controlled. In finding the optimal strategy for the covariance of the controller noise, the solution by means of the calculus of variations involves a singular arc.