Hamed Hossein Afshari/Alireza Basohbat Novinzadeh/Jafar Roshanian
The Journal of Mechanical Science and Technology, vol. 23, no. 12, pp.3239-3244, 2009

Abstract : An optimal trajectory design of a module for the planetary landing problem is achieved by minimizing the control effort expenditure. Using the calculus of variations theorem, the control variable is expressed as a function of costate variables, and the problem is converted into a two-point boundary-value problem. To solve this problem, the performance measure is approximated by employing a trigonometric series and subsequently, the optimal control and state trajectories are determined. To validate the accuracy of the proposed solution, a numerical method of the steepest descent is utilized. The main objective of this paper is to present a novel analytic guidance law of the planetary landing mission by optimizing the control effort expenditure. Finally, an example of a lunar landing mission is demonstrated to examine the results of this solution in practical situations.

Keyword : Nonlinear optimal control; Analytic solution; Control effort expenditure