# Online Dynamics Learning for Predictive Control with an Application to Aerial Robots

arXiv: https://arxiv.org/abs/2207.09344 · HTML: https://mlsanity.com/paper/2207.09344/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 21 of 21)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Online Learning: A Comprehensive Survey](https://mlsanity.com/paper/1802.02871/) (2018)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Low Level Control of a Quadrotor with Deep Model-Based Reinforcement Learning](https://mlsanity.com/paper/1901.03737/) (2019)
- [Data-Driven MPC for Quadrotors](https://mlsanity.com/paper/2102.05773/) (2021)
- [Online Learning for Time Series Prediction](https://mlsanity.com/paper/1302.6927/) (2013)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems](https://mlsanity.com/paper/2002.05514/) (2020)
- [Performance, Precision, and Payloads: Adaptive Nonlinear MPC for Quadrotors](https://mlsanity.com/paper/2109.04210/) (2021)
- [How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification](https://mlsanity.com/paper/1905.08061/) (2019)
- [Knowledge-Based Learning of Nonlinear Dynamics and Chaos](https://mlsanity.com/paper/2010.03415/) (2020)
- [Asynchronous Deep Model Reference Adaptive Control](https://mlsanity.com/paper/2011.02920/) (2020)
- [Derivative-free online learning of inverse dynamics models](https://mlsanity.com/paper/1809.05074/) (2018)
- [Locally Weighted Regression Pseudo-Rehearsal for Online Learning of Vehicle Dynamics](https://mlsanity.com/paper/1905.05162/) (2019)
- [L1 Adaptive Augmentation for Geometric Tracking Control of Quadrotors](https://mlsanity.com/paper/2109.06998/) (2021)
- [Online Simultaneous Semi-Parametric Dynamics Model Learning](https://mlsanity.com/paper/1910.04297/) (2019)
- [Online Weight-adaptive Nonlinear Model Predictive Control](https://mlsanity.com/paper/2008.02532/) (2020)
- [Iterative Semi-parametric Dynamics Model Learning For Autonomous Racing](https://mlsanity.com/paper/2011.08750/) (2020)

## Built on by (most cited first, 17 of 17)

- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotors](https://mlsanity.com/paper/2606.23444/) (2026)
- [Bridging Active Exploration and Uncertainty-Aware Deployment Using Probabilistic Ensemble Neural Network Dynamics](https://mlsanity.com/paper/2305.12240/) (2023)
- [Learning Globally Smooth Functions on Manifolds](https://mlsanity.com/paper/2210.00301/) (2022)
- [Action Flow Matching for Continual Robot Learning](https://mlsanity.com/paper/2504.18471/) (2025)
- [Adaptive Asynchronous Control Using Meta-learned Neural Ordinary Differential Equations](https://mlsanity.com/paper/2207.12062/) (2022)
- [ASV Station Keeping under Wind Disturbances using Neural Network Simulation Error Minimization Model Predictive Control](https://mlsanity.com/paper/2310.07892/) (2023)
- [Learning Based NMPC Adaptation for Autonomous Driving using Parallelized Digital Twin](https://mlsanity.com/paper/2402.16645/) (2024)
- [Flying Quadrotors in Tight Formations using Learning-based Model Predictive Control](https://mlsanity.com/paper/2410.09727/) (2024)
- [Knowledge-based Neural Ordinary Differential Equations for Cosserat Rod-based Soft Robots](https://mlsanity.com/paper/2408.07776/) (2024)
- [Learning Causal Structure Distributions for Robust Planning](https://mlsanity.com/paper/2508.06742/) (2025)
- [Learning-enhanced Nonlinear Model Predictive Control using Knowledge-based Neural Ordinary Differential Equations and Deep Ensembles](https://mlsanity.com/paper/2211.13829/) (2022)
- [Leveraging Predictive Models for Adaptive Sampling of Spatiotemporal Fluid Processes](https://mlsanity.com/paper/2304.00732/) (2023)
- [Proto-MPC: An Encoder-Prototype-Decoder Approach for Quadrotor Control in Challenging Winds](https://mlsanity.com/paper/2401.15508/) (2024)
- [AD-NODE: Adaptive Dynamics Learning with Neural ODEs for Mobile Robots Control](https://mlsanity.com/paper/2510.05443/) (2025)
- [T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics](https://mlsanity.com/paper/2605.24852/) (2026)
- [A Continual Validation, Updating, and Decision-Making Framework for Self-Adaptive Digital Twins via Robust Model Predictive Control: A Case Study in Additive Manufacturing](https://mlsanity.com/paper/2607.18164/) (2026)

## Abstract (arXiv)

In this work, we consider the task of improving the accuracy of dynamic models for model predictive control (MPC) in an online setting. Although prediction models can be learned and applied to model-based controllers, these models are often learned offline. In this offline setting, training data is first collected and a prediction model is learned through an elaborated training procedure. However, since the model is learned offline, it does not adapt to disturbances or model errors observed during deployment. To improve the adaptiveness of the model and the controller, we propose an online dynamics learning framework that continually improves the accuracy of the dynamic model during deployment. We adopt knowledge-based neural ordinary differential equations (KNODE) as the dynamic models, and use techniques inspired by transfer learning to continually improve the model accuracy. We demonstrate the efficacy of our framework with a quadrotor, and verify the framework in both simulations and physical experiments. Results show that our approach can account for disturbances that are possibly time-varying, while maintaining good trajectory tracking performance.