Improved model order reduction techniques with error bounds.

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

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