# Learning-enhanced Nonlinear Model Predictive Control using Knowledge-based Neural Ordinary Differential Equations and Deep Ensembles

arXiv: https://arxiv.org/abs/2211.13829 · HTML: https://mlsanity.com/paper/2211.13829/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 24 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Data-Driven MPC for Quadrotors](https://mlsanity.com/paper/2102.05773/) (2021)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking](https://mlsanity.com/paper/2206.03305/) (2022)
- [Online Dynamics Learning for Predictive Control with an Application to Aerial Robots](https://mlsanity.com/paper/2207.09344/) (2022)
- [Knowledge-Based Learning of Nonlinear Dynamics and Chaos](https://mlsanity.com/paper/2010.03415/) (2020)
- [A nonlinear model predictive control framework using reference generic terminal ingredients -- extended version](https://mlsanity.com/paper/1909.12765/) (2019)

## Abstract (arXiv)

Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem, subjected to a set of dynamics constraints characterized by a nonlinear dynamics model, is solved at each time step. Despite its versatility, the performance of nonlinear MPC often depends on the accuracy of the dynamics model. In this work, we leverage deep learning tools, namely knowledge-based neural ordinary differential equations (KNODE) and deep ensembles, to improve the prediction accuracy of this model. In particular, we learn an ensemble of KNODE models, which we refer to as the KNODE ensemble, to obtain an accurate prediction of the true system dynamics. This learned model is then integrated into a novel learning-enhanced nonlinear MPC framework. We provide sufficient conditions that guarantees asymptotic stability of the closed-loop system and show that these conditions can be implemented in practice. We show that the KNODE ensemble provides more accurate predictions and illustrate the efficacy and closed-loop performance of the proposed nonlinear MPC framework using two case studies.