Implicit Higher-Order Moment Matching Technique for Model Reduction of Quadratic-bilinear Systems

TL;DR

This paper introduces a novel projection-based multi-moment matching method for quadratic-bilinear system model reduction, achieving higher-order moment matching with improved efficiency over existing techniques.

Contribution

It extends the moment matching framework to the regular form, enabling matching of the first three multivariate transfer functions, which was not previously possible.

Findings

Better performance on benchmark examples

Reduced computational cost

Enhanced moment matching accuracy

Abstract

We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions appearing in the input-output representation of the nonlinear system. An existing technique achieves this for the first two multivariate transfer functions, in what is called the symmetric form of the multivariate transfer functions. We extend this framework to an equivalent and simplified form, the regular form, which allows us to show moment matching for the first three multivariate transfer functions. Numerical results for three benchmark examples of quadratic-bilinear systems show that the proposed framework exhibits better performance with reduced computational cost in comparison to existing techniques.