Frequency-weighted H2-Pseudo-optimal Model Order Reduction

TL;DR

This paper introduces efficient algorithms for frequency-weighted H2-pseudo-optimal model order reduction, ensuring stability and partial optimality, validated through numerical examples.

Contribution

It proposes two iteration-free algorithms for single-sided cases and an iterative method for double-sided cases, improving computational efficiency and partial optimality in model reduction.

Findings

Algorithms ensure stability of reduced models.

Validated on three numerical examples.

Achieve computational efficiency over existing methods.

Abstract

The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we investigate the frequency-weighted H2-pseudo-optimal model order reduction problem wherein a subset of the optimality conditions for the local optimum is attempted to be satisfied. We propose two iteration-free algorithms, for the single-sided frequency-weighted case of H2-model reduction, where a subset of the optimality conditions is ensured by the reduced system. In addition, the reduced systems retain the stability property of the original system. We also present an iterative algorithm for the double-sided frequency-weighted case, which constructs a reduced-order model that tends to satisfy a subset of the first-order optimality conditions for the local optimum. The proposed algorithm is computationally efficient as compared to the existing algorithms. We validate the theory developed in this paper on three numerical examples.