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# A Machine Learning Enhanced Algorithm for the Optimal Landing Problem

*Proceedings of Mathematical and Scientific Machine Learning*, PMLR 190:319-334, 2022.

#### Abstract

We propose a machine learning enhanced algorithm for solving the optimal landing problem. Using Pontryagin’s minimum principle, we derive a two-point boundary value problem for the landing problem. The proposed algorithm uses deep learning to predict the optimal landing time and a space-marching technique to provide good initial guesses for the boundary value problem solver. The performance of the proposed method is studied using the quadrotor example, a reasonably high dimensional and strongly nonlinear system. Drastic improvement in reliability and efficiency is observed.