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

2025-04-28

AI Summary

This work addresses the lack of stability guarantees in neural control of mechanical systems by proposing a Negative Imaginary (NI)-based Neural Ordinary Differential Equation (NINODE) controller. Methodologically, it embeds a structured neural network into a Hamiltonian state-space model, ensuring the closed-loop system inherently satisfies the NI frequency-domain condition; crucially, it formulates the NI stability requirement as a regularized constraint on neural network weights, unifying data-driven control design with rigorous stability certification. The key contribution is the first verifiable NI-preserving neural ODE architecture, integrating NI systems theory, Hamiltonian modeling, and physics-informed training. Experimental validation on a nonlinear spring-mass system demonstrates that the controller achieves asymptotic stability without online optimization, while exhibiting strong robustness and real-time capability.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Guaranteed stabilization for mechanical systems using NINODE
• Ensuring NI property via Hamiltonian neural networks
• Stability constraints translated into neural network regularity

Innovation

• Neural ODE controller ensures mechanical system stability
• Hamiltonian framework enforces negative imaginary properties
• Regularity constraints on neural networks guarantee stability