Solving The Optimization Control Problem For Lunar Soft Landing Using Minimization Technique
Abstract
Minimizing fuel consumption in lunar missions has been a well studied and documented optimization problem. In this paper two cases of the lunar Lander are studied. The first case is the one dimensional problem where the objective is to make a vertical soft landing using the minimum amount of fuel. The second case has the same objective but an initial tangential velocity greater than zero is given making it a two dimensional problem. The first case is solved using Newton's shooting method, finite difference method (using MATLAB's embedded function bvp4c), and solving it explicitly. For the second case, a minimization technique is proposed for cases where the above methods fail to provide a solution.