Nonlinear Optimal Closed-Loop Guidance Law for Lunar Landing Mission Using Perturbation Feedback Control

An optimal trajectory design of a nonlinear lunar landing mission for soft landing on the moon by minimizing the landing time is reported in this paper. It is an exact solution to the two-point boundary value problem which determines the state variables and optimal control history in the open-loop form by satisfying the terminal conditions. Furthermore, in this paper the lunar landing mission is closed-loop against the environment disturbances by using of optimal open-loop solution and applying an analytical method named perturbation feedback control. By using the perturbation feedback method based on the calculus of variations theory, one can compute the feedback control law for nonlinear lunar landing mission in each instant of time. This law is a function of states perturbation and constraints perturbation which can minimize the landing time and satisfy the terminal conditions appropriately.