# Improving the Region of Attraction of a Multi-rotor UAV by Estimating Unknown Disturbances

arXiv: https://arxiv.org/abs/2409.00257 · HTML: https://mlsanity.com/paper/2409.00257/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 7 of 7)

- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes](https://mlsanity.com/paper/1603.04915/) (2016)
- [NeuralSens: Sensitivity Analysis of Neural Networks](https://mlsanity.com/paper/2002.11423/) (2020)
- [Deep Neural Networks for Improved, Impromptu Trajectory Tracking of Quadrotors](https://mlsanity.com/paper/1610.06283/) (2016)
- [Learn Fast, Forget Slow: Safe Predictive Learning Control for Systems with Unknown and Changing Dynamics Performing Repetitive Tasks](https://mlsanity.com/paper/1810.06681/) (2018)
- [Controller design and region of attraction estimation for nonlinear dynamical systems](https://mlsanity.com/paper/1310.2213/) (2013)

## Abstract (arXiv)

This study presents a machine learning-aided approach to accurately estimate the region of attraction (ROA) of a multi-rotor unmanned aerial vehicle (UAV) controlled using a linear quadratic regulator (LQR) controller. Conventional ROA estimation approaches rely on a nominal dynamic model for ROA calculation, leading to inaccurate estimation due to unknown dynamics and disturbances associated with the physical system. To address this issue, our study utilizes a neural network to predict these unknown disturbances of a planar quadrotor. The nominal model integrated with the learned disturbances is then employed to calculate the ROA of the planer quadrotor using a graphical technique. The estimated ROA is then compared with the ROA calculated using Lyapunov analysis and the graphical approach without incorporating the learned disturbances. The results illustrated that the proposed method provides a more accurate estimation of the ROA, while the conventional Lyapunov-based estimation tends to be more conservative.