Iterative Stability Enforcement in Adaptive Antoulas–Anderson Algorithms for ${\boldsymbol{\mathcal{H}_2}}$ Model Reduction

Davis, Lisa; Johns, William; Monzón, Lucas; Reynolds, Matthew

doi:10.1137/21m1467043

Iterative Stability Enforcement in Adaptive Antoulas–Anderson Algorithms for ${\boldsymbol{\mathcal{H}_2}}$ Model Reduction

Journal Article · 20 July 2023 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/21m1467043· OSTI ID:2005602

Davis, Lisa ^[1]; ^[2]; Monzón, Lucas ^[3]; Reynolds, Matthew ^[4]

Department of Mathematics, Montana State University, Bozeman, MT 59717 USA.
Pacific Northwest National Lab, Richland, WA 99354 USA.
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309 USA.
National Renewable Energy Lab, Golden, CO 80401 USA.

This paper presents an extension of the Adaptive-Antoulas-Anderson (AAA) algorithm for rational modelling. Specifically, our new stable multi-input multi-output AAA (smiAAA) algorithm builds rational approximations of multi-input signals with a common set of stable poles. A new methodology is presented for iteratively enforcing stability constraints on the poles. We demonstrate the strengths of this approach compared to the stability enforcement in the FastAAA algorithm. Results using the smiAAA algorithm are compared with the commonly used Vector Fitting algorithm and the more recently published RKFIT algorithm. Vector Fitting and RKFIT both require the user to input the number of poles to use in the approximations. If the final approximation is not accurate enough, the user must re-start Vector Fitting or RKFIT with a larger number of poles and/or a new starting location for the poles. In contrast, the smiAAA algorithm is designed to allow the user to simply input the desired accuracy of the approximations, and the necessary number of poles is detected automatically. This permits users to produce approximations of a desired accuracy with no knowledge about the underlying order of the system being approximated, preventing the algorithm from ever needing to be rerun. An additional feature for preventing extraneous poles from being returned by AAA is also discussed. The cause of these extraneous poles is efficiently detected and removed by our presented methodology. In conclusion, the examples presented demonstrate that smiAAA can efficiently produce approximations of similar or better accuracy than Vector Fitting and RKFIT while requiring less input from the user.

View Accepted Manuscript (DOE)

Research Organization:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Organization:: USDOE Office of Energy Efficiency and Renewable Energy (EERE), Renewable Power Office. Solar Energy Technologies Office; National Science Foundation (NSF)

Grant/Contract Number:: AC36-08GO28308

OSTI ID:: 2005602

Alternate ID(s):: OSTI ID: 2274746

Report Number(s):: NREL/JA--2C00-81453; MainId:82226; UUID:9f0de04c-623f-4417-a34c-cc52fb79101f; MainAdminId:70763

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 4 Vol. 45; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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