# A Machine Learning Enhanced Algorithm for the Optimal Landing Problem

arXiv: https://arxiv.org/abs/2203.06753 · HTML: https://mlsanity.com/paper/2203.06753/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2022.

## Built on by (most cited first, 4 of 4)

- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Offline Supervised Learning V.S. Online Direct Policy Optimization: A Comparative Study and A Unified Training Paradigm for Neural Network-Based Optimal Feedback Control](https://mlsanity.com/paper/2211.15930/) (2022)
- [Neural Network Optimal Feedback Control with Guaranteed Local Stability](https://mlsanity.com/paper/2205.00394/) (2022)
- [Neural Co-state Projection Regulator: A Model-free Paradigm for Real-time Optimal Control with Input Constraints](https://mlsanity.com/paper/2508.00283/) (2025)

## Abstract (arXiv)

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.