@article{Kim2026, 
author = {Mingyu Kim and Sukyung Seo and Suhwan Choi and Yeongjae Kim and Yeongmi Kim and Tae-Hyoung Kim},
title = {Model order reduction using dual    ν-gap metrics: A multi-objective optimization approach},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {1},
pages = {433-462},
keywords = {model order reduction, ν-gap metric, parameter identification, particle swarm optimization, multi-objective optimization},
url = {https://www.sciopen.com/article/10.3934/era.2026021},
doi = {10.3934/era.2026021},
abstract = {This study investigated the problem of model order reduction by employing the    ν-gap metric and introduced a metaheuristic optimization framework to address its inherent nonconvexity. The    ν-gap metric quantifies the closed-loop distance between two systems, making it useful for generating low-order models that preserve closed-loop stability characteristics. However, minimizing the conventional    ν-gap alone may result in poor dynamic fidelity. To address this limitation, a modified    ν-gap metric based on frequency response matching was developed to explicitly capture frequency-wise discrepancies associated with time-domain behavior. By jointly considering the conventional and modified    ν-gap metrics, a dual    ν-gap–based multi-objective model reduction framework was formulated, in which stability-related and time-domain fidelity objectives are treated in a complementary manner. The resulting optimization problem is highly nonconvex and constrained due to the winding number condition. A multi-objective particle swarm optimization framework was therefore employed as a numerical tool to generate Pareto-optimal reduced-order models. Benchmark studies on large-scale systems demonstrated that the proposed framework enables a systematic exploration of trade-offs between stability preservation and time-domain fidelity, yielding practically meaningful reduced-order models with tunable performance characteristics.}
}