Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems

TL;DR

This paper introduces a structure-preserving model reduction method for large-scale port-Hamiltonian systems using tangential rational interpolation, ensuring passivity and efficiency.

Contribution

It develops a novel framework that maintains port-Hamiltonian structure during model reduction and introduces an $\\mathcal{H}_2$-inspired algorithm for optimal interpolation point selection.

Findings

Reduced models are passive and structure-preserving.

The method outperforms existing techniques in quality.

The approach is computationally efficient.

Abstract

Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian systems via tangential rational interpolation. The resulting reduced-order model not only is a rational tangential interpolant but also retains the port-Hamiltonian structure; hence is passive. This reduction methodology is described in both energy and co-energy system coordinates. We also introduce an $\mathcal{H}_2$-inspired algorithm for effectively choosing the interpolation points and tangential directions. The algorithm leads a reduced port-Hamiltonian model that satisfies a subset of $\mathcal{H}_2$-optimality conditions. We present several numerical examples that illustrate the effectiveness of the proposed method showing that it outperforms other existing techniques in both quality and numerical efficiency.