Optimal soft landing control for moon lander

This paper considers the soft landing problem of a moon lander. The main purpose is to design the optimal control law to ensure the soft landing of the lander with the least fuel consumption. It is formulated as a constrained optimal control problem, where specific requirements of this soft landing problem are all incorporated in the problem formulation. Then, by utilizing the specific features of the problem, this optimal soft landing problem is transformed into an equivalent standard optimal control problem subject to continuous state inequality constraints. A computational method is developed, based on the control parameterization in conjunction with a time scaling transform and the constraint transcription method, to design the optimal controller for this new constrained optimal control problem. Numerical results are presented for illustration.