Optimal Control Approach to Soft Landing

First, the history of space explorations is reviewed briefly in this paper alongside with current successful and future missions in this field. Then,missions with landing on celestial bodies, especiallyMoon and Mars landings, and their technical problems and mission challenges are reviewed. Then, as one of the requirements for landing missions, the soft landing problem is introduced in details. As a specialcase, the soft landing on the Moon with mission phases and other system requirements is presented. Due to the importance of fuel saving in the space, the soft landing problem on Moon is modeled as a minimum fuel optimal control problem with nonlinear ordinary differential equations. The governing equations, initial and final conditions in various cases and common performance index formulations are also given based on the recentreferences. Finally, the results of a numerical simulation in a test case problem of Moon landing arereviewed.