Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems

TL;DR

This paper develops structure-preserving interpolatory model reduction techniques for large-scale port-Hamiltonian differential-algebraic systems, effectively handling various system indices while maintaining system properties.

Contribution

It introduces regularization and data selection strategies for interpolatory reduction tailored to port-Hamiltonian DAE systems, including index-1 and index-2 cases.

Findings

Effective reduction of large-scale port-Hamiltonian systems

Preservation of system structure and constraints

Successful numerical examples demonstrating method efficacy

Abstract

We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural features of the system. We introduce approaches that incorporate regularization together with prudent selection of interpolation data. We focus on linear time-invariant systems and present a systematic treatment of a variety of model classes that include combinations of index-$1$ and index-$2$ systems, describing in particular how constraints may be represented in the transfer function and then preserved with interpolatory methods. We propose an algorithm to generate effective interpolation data and illustrate its effectiveness via two numerical examples.