Proportional navigation and the game of two cars (Q1108952)

A stochastic version of Isaacs's game of two cars is considered. The motion of the players is confined to the pursuer's effective operation zone \(D_ P\), and the cost function of the game is the probability of the event: \(\{\) Before the evader enters his safe zone, the evader enters the pursuer's killing zone \(K_ P\), at some t, \(0\leq t\leq T\), or the evader stays in the domain \(D_ P-K_ P\), for all \(t\in [0,t_ 0]\), \(t_ 0>T\}\). By numerically solving a nonlinear parabolic boundary-value problem on a generalized torus in \({\mathbb{R}}^ 3\), it is shown that, for a range of values of some parameter, a proportional navigation guidance law is an optimal feedback pursuit strategy.