Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems

TL;DR

This paper introduces a structure-preserving model reduction method for port-Hamiltonian descriptor systems using a modified Riccati equation approach, providing error bounds and improved model quality through extremal solutions.

Contribution

It develops a novel balanced truncation technique based on dual Riccati equations and a new procedure leveraging the KYP inequality for better model reduction.

Findings

The method preserves system structure and provides error bounds.

Numerical examples show significant quality improvements in reduced models.

The approach effectively handles changes in the Hamiltonian.

Abstract

We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that arise in the context of linear quadratic Gaussian balanced truncation for differential algebraic systems. We derive an a priori error bound with respect to a right coprime factorization of the underlying transfer function thereby allowing for an estimate with respect to the gap metric. We further theoretically and numerically analyze the influence of the Hamiltonian and a change thereof, respectively. With regard to this change of the Hamiltonian, we provide a novel procedure that is based on a recently introduced Kalman-Yakubovich-Popov inequality for descriptor systems. Numerical examples demonstrate how the quality of reduced-order models can significantly be improved by first computing an extremal solution to this inequality.