Optimal fighter pursuit-evasion maneuvers found via two-sided optimization

An optimal pursuit-evasion fighter maneuver is formulated as a differential game and then solved by a recently developed numerical method, semidirect collocation with nonlinear programming. In this method, the optimal control for one player is found numerically, that is, by the optimizer, but that for the other player is based on the analytical necessary conditions of the problem. Because this requires costate variables for one player, the method is not a direct method. However, the problem can be placed in the form of conventional collocation with nonlinear programming. Thus, it is referred to it as a semidirect method. A genetic algorithm is used to provide an approximate solution, an initial guess, for the nonlinear programming problem solver. The method is applied to the challenging problem of optimal fighter aircraft pursuit-evasion in three dimensions. The obtained optimal trajectories are identified as having two phases: first a rapid change, primarily in direction, followed by a period of primarily vertical maneuvering. Solutions for various initial positions and velocities of the evader aircraft with respect to the pursuer are determined.