Balancing-based model reduction for switched descriptor systems
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909171485507584 |
|---|---|
| author | Manucci, Mattia Unger, Benjamin |
| author_facet | Manucci, Mattia Unger, Benjamin |
| contents | We present a novel certified model order reduction (MOR) algorithm for switched descriptor systems applicable to large-scale systems. Our algorithm combines the idea of [Hossain \& Trenn, Technical report, 2023] to reformulate the switched descriptor system as a switched ordinary differential equation with jumps and an extension of the balanced truncation for switched ODE from [Pontes Duff et al., IEEE Trans.~Automat.~Control, 2020]. Besides being the first MOR method for switched descriptor systems applicable to the large-scale setting, we give a detailed numerical analysis by incorporating the error in the computation of the system Gramians in the a-priori error bound for the output of the reduced system. In more detail, we demonstrate, theoretically and numerically, that the standard error bound is not applicable, and a certificate must account for the numerical approximation errors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Balancing-based model reduction for switched descriptor systems Manucci, Mattia Unger, Benjamin Numerical Analysis 65F45, 65F55, 65P99, 93A30, 93A15, 93B99 We present a novel certified model order reduction (MOR) algorithm for switched descriptor systems applicable to large-scale systems. Our algorithm combines the idea of [Hossain \& Trenn, Technical report, 2023] to reformulate the switched descriptor system as a switched ordinary differential equation with jumps and an extension of the balanced truncation for switched ODE from [Pontes Duff et al., IEEE Trans.~Automat.~Control, 2020]. Besides being the first MOR method for switched descriptor systems applicable to the large-scale setting, we give a detailed numerical analysis by incorporating the error in the computation of the system Gramians in the a-priori error bound for the output of the reduced system. In more detail, we demonstrate, theoretically and numerically, that the standard error bound is not applicable, and a certificate must account for the numerical approximation errors. |
| title | Balancing-based model reduction for switched descriptor systems |
| topic | Numerical Analysis 65F45, 65F55, 65P99, 93A30, 93A15, 93B99 |
| url | https://arxiv.org/abs/2404.10511 |