Structure-Preserving Model Order Reduction for Index One Port-Hamiltonian Descriptor Systems

TL;DR

This paper introduces an optimization-based model order reduction method that preserves the port-Hamiltonian structure of index-one descriptor systems, improving accuracy and handling algebraic constraints effectively.

Contribution

It presents a novel optimization framework for structure-preserving MOR of pH descriptor systems, enhancing existing projection-based methods.

Findings

Higher accuracy of reduced models demonstrated in numerical examples.

Simplified treatment of algebraic constraints in pH systems.

Effective preservation of port-Hamiltonian structure during reduction.

Abstract

We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems in pH form permit energy-based modeling and intuitive coupling of physical systems across different physical domains, scales, and accuracies. This makes pH models well-suited building-blocks for component-wise modeling of large system networks. In this context, it is often necessary to preserve the pH structure during MOR. We discuss current projection-based and structure-preserving MOR algorithms for pH systems and present a new optimization-based framework for that task. The benefits of our method include a simplified treatment of algebraic constraints and often a higher accuracy of the resulting reduced-order model, which is demonstrated by several numerical examples.