Trajectory optimization using fast-time repetitive computation

Space vehicle trajectories must be near optimum in the sense that some parameter is either a maximum or a minimum; for example, in reentry the trajectory to desired terminal conditions is near optimum when the total aerodynamic heating is a minimum. Several perturbation methods, such as the calculus of variations, applications of the maximum principle, and direct steepest descent, have been considered for determining the time histories of nonlinear controls that correspond to optimum trajectories.