Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems

TL;DR

This paper introduces a neural network approach for data-driven modeling of port-Hamiltonian systems that preserves their structure and stability, allowing for more flexible Hamiltonian representations and multiple stable equilibria.

Contribution

It relaxes the convexity constraint in neural Hamiltonian approximation, enabling more expressive models that better preserve system stability and structure.

Findings

The proposed method achieves higher accuracy in modeling port-Hamiltonian systems.

It effectively preserves multiple stable equilibria in learned models.

Numerical experiments validate improved structure and stability preservation.

Abstract

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling technique that relaxes the convexity constraint commonly imposed by neural network-based Hamiltonian approximations, thereby improving the expressiveness and generalization capability of the model. By removing this restriction, the proposed approach enables the use of more general non-convex Hamiltonian representations to enhance modeling flexibility and accuracy. Furthermore, the proposed method incorporates information about stable equilibria into the learning process, allowing the learned model to preserve the stability of multiple isolated equilibria rather than being restricted to a single equilibrium as in conventional methods. Two numerical experiments are conducted to validate the effectiveness of the proposed approach and demonstrate its ability to achieve more accurate structure- and stability-preserving learning of port-Hamiltonian systems compared with a baseline method.