Fast Desensitized Optimal Control for Rocket-Powered Descent and Landing

Abstract

This research revisits Desensitized Optimal Control Theory (DOC) for its application to a computationally challenging benchmark: a rocket descent and landing scenario. The primary objective is to assess the efficacy of the proposed method in mitigating the impact of perturbations on the final state, thereby establishing a framework capable of simultaneously optimizing guidance and control for the specified case. Additionally, our focus is on formulating a rapid and computationally efficient approach to enhance speed without compromising accuracy. The investigation begins with a comprehensive analysis of the fundamental components of the method, particularly the sensitivity terms and the computation of feedback gains, with a comparison of alternative formulations to evaluate their relative computational efficiency. Subsequently, the application of this methodology to the target problem is thoroughly examined with an a-priori performance index and characterized to reach the most efficient formulation, through the introduction of the idea of \emph{dominant sensitivities}. Case-dependent modifications are explained and implemented to improve the methodology performances, resulting in the introduction of the \emph{Marginal {DOC} Coefficient}, and the results are critically compared against those obtained using conventional methods through an extensive Monte Carlo analysis campaign.