Frequency-weighted H2-optimal model order reduction via oblique projection

TL;DR

This paper introduces a projection-based algorithm for frequency-weighted H2-optimal model order reduction that nearly satisfies optimality conditions and improves computational efficiency, demonstrated through numerical examples.

Contribution

A novel algorithm for frequency-weighted H2-optimal model reduction using oblique projection that approaches optimality with increasing model order.

Findings

Algorithm nearly satisfies first-order optimality conditions.

Deviations decrease as model order increases.

Numerical examples confirm effectiveness and efficiency.

Abstract

In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto a reduced subspace that contains its dominant characteristics. The problem of frequency-weighted H2-optimal model order reduction is to construct a local optimum in terms of the H2-norm of the weighted error transfer function. In this paper, a projection-based model order reduction algorithm is proposed that constructs reduced-order models that nearly satisfy the first-order optimality conditions for the frequency-weighted H2-optimal model order reduction problem. It is shown that as the order of the reduced model is increased, the deviation in the satisfaction of the optimality conditions reduces further. Numerical methods are also discussed that improve the computational efficiency of the proposed algorithm. Three numerical examples are presented to demonstrate the efficacy of the proposed algorithm.