Nonlinear optimal feedback control for lunar module soft landing

In this paper, the optimal control problem to achieve lunar module soft landing with least fuel consumption is considered. The precise three dimensional dynamics is employed to describe the motion of the lunar module. By introducing two new state equations, a closed loop optimal control law is designed with a parameter matrix K to be determined which is the solution of a riccati like differential equation. We present a practical method to calculate the matrix K, such that it is avoided to solve the complex riccati like differential equation. Simulation results show the efficiency of the proposed method.