Data-driven balanced truncation of K-power bilinear systems
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.
Keywords
Cite
@article{arxiv.2604.11268,
title = {Data-driven balanced truncation of K-power bilinear systems},
author = {Xiaolong Wang and Biaolin Li and Xiaoli Wang},
journal= {arXiv preprint arXiv:2604.11268},
year = {2026}
}