Robust Nonlinear Optimal Solution to the Lunar Landing Guidance by Using Neighboring Optimal Control

Abstract

A closed-loop time-optimal control strategy for the highly nonlinear problem of the lunar landing mission by using the perturbation technique is developed in this study. The first part of the study considers analytical solution for an optimal control policy of variable mass spacecraft, while it descents on the surface of the moon in the variable gravitational field of it. To validate the accuracy of perturbation solution, a numerical approach based on steepest descent method is employed. The second part considers analytical derivation of an optimal feedback guidance solution by employing the neighboring optimal control (NOC) law when effects of imperfection in the dynamic model or disturbing noises have been taken into account. The technique of NOC produces time-varying feedback gains that minimize the performance index to the second order for perturbations from a nominal optimal path. The robustness of the designed NOC law is examined with applying sinusoidal noises. From the study of the simulation results, it may be concluded that the developed optimal guidance laws may be used in real world spacecraft applications.