# Neural ODEs as Feedback Policies for Nonlinear Optimal Control

arXiv: https://arxiv.org/abs/2210.11245 · HTML: https://mlsanity.com/paper/2210.11245/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 88 references that are in the map.
- First posted on arXiv 20 Oct 2022.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [Lyapunov-based Safe Policy Optimization for Continuous Control](https://mlsanity.com/paper/1901.10031/) (2019)
- [Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE](https://mlsanity.com/paper/2006.02493/) (2020)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework](https://mlsanity.com/paper/1912.12970/) (2019)
- [Continuous-Time Model-Based Reinforcement Learning](https://mlsanity.com/paper/2102.04764/) (2021)
- [DiffEqFlux.jl - A Julia Library for Neural Differential Equations](https://mlsanity.com/paper/1902.02376/) (2019)
- [Stochastic data-driven model predictive control using Gaussian processes](https://mlsanity.com/paper/1908.01786/) (2019)
- [Chance Constrained Policy Optimization for Process Control and Optimization](https://mlsanity.com/paper/2008.00030/) (2020)
- [Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees](https://mlsanity.com/paper/2004.11184/) (2020)
- [Faster Policy Learning with Continuous-Time Gradients](https://mlsanity.com/paper/2012.06684/) (2020)
- [A Unifying Modeling Abstraction for Infinite-Dimensional Optimization](https://mlsanity.com/paper/2106.12689/) (2021)

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

- [Machine Learning Methods for Small Data and Upstream Bioprocessing Applications: A Comprehensive Review](https://mlsanity.com/paper/2506.12322/) (2025)
- [Continuous-Time Reinforcement Learning: New Design Algorithms with Theoretical Insights and Performance Guarantees](https://mlsanity.com/paper/2307.08920/) (2023)
- [Lyapunov Neural ODE State-Feedback Control Policies](https://mlsanity.com/paper/2409.00393/) (2024)
- [Control of dynamical systems with neural networks](https://mlsanity.com/paper/2510.12810/) (2025)

## Abstract (arXiv)

Neural ordinary differential equations (Neural ODEs) define continuous time dynamical systems with neural networks. The interest in their application for modelling has sparked recently, spanning hybrid system identification problems and time series analysis. In this work we propose the use of a neural control policy capable of satisfying state and control constraints to solve nonlinear optimal control problems. The control policy optimization is posed as a Neural ODE problem to efficiently exploit the availability of a dynamical system model. We showcase the efficacy of this type of deterministic neural policies in two constrained systems: the controlled Van der Pol system and a bioreactor control problem. This approach represents a practical approximation to the intractable closed-loop solution of nonlinear control problems.