# Negative Imaginary Neural ODEs: Learning to Control Mechanical Systems with Stability Guarantees

arXiv: https://arxiv.org/abs/2504.19497 · HTML: https://mlsanity.com/paper/2504.19497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 28 Apr 2025.

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

- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [Interconnections of input-output Hamiltonian systems with dissipation](https://mlsanity.com/paper/1603.04019/) (2016)
- [Learning Stable and Passive Neural Differential Equations](https://mlsanity.com/paper/2404.12554/) (2024)
- [Stability robustness of a feedback interconnection of systems with negative imaginary frequency response](https://mlsanity.com/paper/1401.7739/) (2014)
- [Feedback Control of Negative-Imaginary Systems: Large Flexible structures with colocated actuators and sensors](https://mlsanity.com/paper/1401.7745/) (2014)
- [Physical Interpretations of Negative Imaginary Systems Theory](https://mlsanity.com/paper/1503.01189/) (2015)
- [Robust Output Feedback Consensus for Networked Identical Nonlinear Negative-Imaginary Systems](https://mlsanity.com/paper/2005.11492/) (2020)
- [Output Feedback Consensus for Networked Heterogeneous Nonlinear Negative-Imaginary Systems with Free Body Motion](https://mlsanity.com/paper/2011.14610/) (2020)
- [Necessary and Sufficient Conditions for State Feedback Equivalence to Negative Imaginary Systems](https://mlsanity.com/paper/2109.11273/) (2021)
- [A Nonlinear Negative Imaginary Systems Framework with Actuator Saturation for Control of Electrical Power Systems](https://mlsanity.com/paper/2311.06820/) (2023)

## Abstract (arXiv)

We propose a neural control method to provide guaranteed stabilization for mechanical systems using a novel negative imaginary neural ordinary differential equation (NINODE) controller. Specifically, we employ neural networks with desired properties as state-space function matrices within a Hamiltonian framework to ensure the system possesses the NI property. This NINODE system can serve as a controller that asymptotically stabilizes an NI plant under certain conditions. For mechanical plants with colocated force actuators and position sensors, we demonstrate that all the conditions required for stability can be translated into regularity constraints on the neural networks used in the controller. We illustrate the utility, effectiveness, and stability guarantees of the NINODE controller through an example involving a nonlinear mass-spring system.