# Lyapunov Neural ODE State-Feedback Control Policies

arXiv: https://arxiv.org/abs/2409.00393 · HTML: https://mlsanity.com/paper/2409.00393/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 31 Aug 2024.

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

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework](https://mlsanity.com/paper/1912.12970/) (2019)
- [Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems](https://mlsanity.com/paper/2203.15706/) (2022)
- [LyaNet: A Lyapunov Framework for Training Neural ODEs](https://mlsanity.com/paper/2202.02526/) (2022)
- [Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems](https://mlsanity.com/paper/2011.03699/) (2020)
- [Neural Ordinary Differential Equations for Nonlinear System Identification](https://mlsanity.com/paper/2203.00120/) (2022)
- [Neural Lyapunov Differentiable Predictive Control](https://mlsanity.com/paper/2205.10728/) (2022)
- [Approximate Optimal Control for Safety-Critical Systems with Control Barrier Functions](https://mlsanity.com/paper/2008.04122/) (2020)
- [A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability](https://mlsanity.com/paper/1903.07214/) (2019)
- [Neural ODEs as Feedback Policies for Nonlinear Optimal Control](https://mlsanity.com/paper/2210.11245/) (2022)

## Abstract (arXiv)

Deep neural networks are increasingly used as an effective parameterization of control policies in various learning-based control paradigms. For continuous-time optimal control problems (OCPs), which are central to many decision-making tasks, control policy learning can be cast as a neural ordinary differential equation (NODE) problem wherein state and control constraints are naturally accommodated. This paper presents a NODE approach to solving continuous-time OCPs for the case of stabilizing a known constrained nonlinear system around a target state. The approach, termed Lyapunov-NODE control (L-NODEC), uses a novel Lyapunov loss formulation that incorporates an exponentially-stabilizing control Lyapunov function to learn a state-feedback neural control policy, bridging the gap of solving continuous-time OCPs via NODEs with stability guarantees. The proposed Lyapunov loss allows L-NODEC to guarantee exponential stability of the controlled system, as well as its adversarial robustness to perturbations to the initial state. The performance of L-NODEC is illustrated in two problems, including a dose delivery problem in plasma medicine. In both cases, L-NODEC effectively stabilizes the controlled system around the target state despite perturbations to the initial state and reduces the inference time necessary to reach the target.