An exact penalty function method for optimal lunar soft landing control problem

This paper studies the soft landing fuel consumption problem of a moon lander. A dynamics model of the moon lander is established. Based on this model, a constrained optimal control problem is formulated, where specific requirements of the soft landing fuel consumption problem are all incorporated in the optimal control problem. By using the control parametrization technique used conjunction with a time scaling transform and the exact penalty function method, the constrained optimal control problem is approximated by a sequence of approximate unconstrained optimization problems. It is shown that the solutions of these approximate unconstrained optimization problems converge to the solution of the original problem. A numerical algorithm is provided to solve these these approximate unconstrained optimization problems. Finally, the effectiveness of the proposed method is demonstrated through solving the lunar soft landing problem with the minimum fuel consumption.