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Improved model order reduction techniques with error bounds.

Bashrat, Shabana; Imran, Muhammad; Akram, Safia; Wakeel, Abdul; Baig, Nauman Anwar; Zaheer Ud-Din, Asim

Authors

Shabana Bashrat

Muhammad Imran

Safia Akram

Abdul Wakeel

Asim Zaheer Ud-Din



Abstract

This paper introduces two enhanced model order reduction techniques designed for scenarios involving frequency-weighted and frequency-limited-interval Gramians in the continuous-time domain. The primary objective is to address the instability issue identified in existing approaches in the continuous-time domain, as formulated by Enns for frequency-weighted scenarios and Gawronski & Juang for frequency-limited-interval scenarios. Despite numerous solutions proposed in the literature to mitigate this problem, a persistent challenge remains the high approximation error between the original and reduced-order systems. To overcome this limitation, the proposed improved techniques focus on ensuring stability in reduced-order models while simultaneously minimising the approximation error between the original and reduced systems. Furthermore, these enhanced techniques provide a computationally straightforward, a priori error bound formula. Numerical findings underscore the correctness and efficiency of the proposed techniques in reducing the approximation error while maintaining stability, thereby substantiating their efficacy.

Citation

BASHRAT, S., IMRAN, M., AKRAM, S., WAKEEL, A., BAIG, N.A. and UD-DIN, A.Z. 2024. Improved model order reduction techniques with error bounds. International journal of systems science [online], 55(4), pages 687-700. Available from: https://doi.org/10.1080/00207721.2023.2293683

Journal Article Type Article
Acceptance Date Dec 6, 2023
Online Publication Date Dec 22, 2023
Publication Date Mar 11, 2024
Deposit Date Mar 18, 2024
Publicly Available Date Dec 23, 2024
Journal International journal of systems science
Print ISSN 0020-7721
Electronic ISSN 1464-5319
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
Volume 55
Issue 4
Pages 687-700
DOI https://doi.org/10.1080/00207721.2023.2293683
Keywords Reduced-order model; Frequency-limited-interval; Frequency-weights; Gramians; Error bound
Public URL https://rgu-repository.worktribe.com/output/2278524