An iterative tangential interpolation algorithm for model reduction of MIMO systems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908863795560448 |
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| author | Jonas, Jared Bamieh, Bassam |
| author_facet | Jonas, Jared Bamieh, Bassam |
| contents | We consider model reduction of large-scale multi-input, multi-output (MIMO) systems using tangential interpolation in the frequency domain. Our scheme is related to the recently-developed Adaptive Antoulas--Anderson (AAA) algorithm, which is an iterative algorithm that uses concepts from the Loewner framework. Our algorithm has two main features. The first is the use of freedom in interpolation weight matrices to optimize a proxy for an \(H_2\) system error. The second is the use of low-rank interpolation, where we iteratively add low-order interpolation data based on several criteria including minimizing maximum errors. We show there is freedom in the interpolation point selection method, leading to multiple algorithms that have trade-offs between computational complexity and approximation performance. We prove that a weighted \(H_2\) norm of a representative error system is monotonically decreasing as interpolation points are added. Finally, we provide computational results and some comparisons with prior work, demonstrating performance on par with standard model reduction methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An iterative tangential interpolation algorithm for model reduction of MIMO systems Jonas, Jared Bamieh, Bassam Systems and Control We consider model reduction of large-scale multi-input, multi-output (MIMO) systems using tangential interpolation in the frequency domain. Our scheme is related to the recently-developed Adaptive Antoulas--Anderson (AAA) algorithm, which is an iterative algorithm that uses concepts from the Loewner framework. Our algorithm has two main features. The first is the use of freedom in interpolation weight matrices to optimize a proxy for an \(H_2\) system error. The second is the use of low-rank interpolation, where we iteratively add low-order interpolation data based on several criteria including minimizing maximum errors. We show there is freedom in the interpolation point selection method, leading to multiple algorithms that have trade-offs between computational complexity and approximation performance. We prove that a weighted \(H_2\) norm of a representative error system is monotonically decreasing as interpolation points are added. Finally, we provide computational results and some comparisons with prior work, demonstrating performance on par with standard model reduction methods. |
| title | An iterative tangential interpolation algorithm for model reduction of MIMO systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2506.03410 |