Optimal strategies in the neighborhood of a collision course

We consider a simple differential game between pursuer P and evader E in the neighborhood of a nominal collision course. The payoff is the terminal lateral miss-distance. The control of each player is his acceleration normal to his velocity vector, and both players' controls are bounded. Saddlepoint strategies are deduced for three combinations of the acceleration bounds and are shown to be related to the sign of the derivative of the orientation of the line of sight (L.O.S.).