2023/04/07 by Annan Yu, Alex Townsend, Yu, Annan +1
Engineering · Mathematics · Physics and Astronomy · #41A20 #65D15 #93C05 #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2304.03813
openalex publication_date 2023/04/07 · openalex created_date 2023/04/15 · openalex updated_date 2026/07/28
Large-scale linear, time-invariant (LTI) dynamical systems are widely used to characterize complicated physical phenomena. We propose a two-stage algorithm to reduce the order of a large-scale LTI system given samples of its transfer function for a target degree k of the reduced system. In the first stage, a modified adaptive Antoulas--Anderson (AAA) algorithm is used to construct a degree d rational approximation of the transfer function that corresponds to an intermediate system, which can be numerically stably reduced in the second stage using ideas from the theory on Hankel norm approximation (HNA). We also study the numerical issues of Glover's HNA algorithm and provide a remedy for its numerical instabilities. A carefully computed rational approximation of degree d gives us a numerically stable algorithm for reducing an LTI system, which is more efficient than SVD-based algorithms and more accurate than moment-matching algorithms.