Data-driven balanced truncation of K-power bilinear systems

TL;DR

This paper introduces a data-driven balanced truncation method for K-power bilinear systems, leveraging transfer function evaluations to efficiently produce reduced models without complex calculations.

Contribution

It develops a novel data-driven approach for balanced truncation of K-power systems, utilizing transfer function evaluations to simplify model reduction.

Findings

Reduced models accurately approximate original systems.

Method avoids complex arithmetic, producing real-valued models.

Numerical examples demonstrate effectiveness and feasibility.

Abstract

As a special type of bilinear systems, K-power bilinear systems possess a special coupled structure along with nice properties in practice. In this paper, we investigate the data-driven counterpart of balanced truncation for K-power systems. As the standard balanced truncation is performed based on the subsystems of K-power systems, the main idea is to approximate the quantities of each reduced subsystem with the evaluations of transfer functions. We exploit the nice properties of Gramians for K-power systems, and establish the explicit relationship between the main quantities of balanced truncation and the evaluation of transfer functions. As a result, reduced models produced via balanced truncation can be assembled approximately by the sample data of transfer functions, leading to a data-driven balancing truncation method for K-power systems. An advanced procedure is also provided to avoid the complex arithmetic completely and produce real-valued reduced models. Two numerical examples confirm the feasibility and effectiveness of the proposed method.