Solution of a Pursuit–Evasion Game Using a Near-Optimal Strategy

The semidirect collocation nonlinear programming method can be used to numerically solve realistic and complex pursuit-evasion problems. Unfortunately, this technique requires an initial guess for the physically unintuitive costates of one of the players. For the scenario where proportional navigation is nearly optimal for the pursuer, this paper proposes solving a one-sided optimal control problem to rapidly estimate the costates, which are then used as the initial guess to obtain a solution to the game using the semidirect nonlinear programming method. To expand the usefulness of the technique, a method of implementing pure state constraints via a penalty function appended to the objective is suggested. A differential game entailing a missile evasion scenario is posed and solved to demonstrate the proposed techniques.