Symplectic model order reduction of port-Hamiltonian systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866915554863874048 |
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| author | Glas, Silke Mamunuzzaman, Mir Mu, Hongliang Zwart, Hans |
| author_facet | Glas, Silke Mamunuzzaman, Mir Mu, Hongliang Zwart, Hans |
| contents | This work proposes a novel structure-preserving model order reduction (MOR) method for linear, time-invariant port-Hamiltonian (pH) systems. Our goal is to construct a reduced order pH system, which can still be interpreted in the physical domain of the full order model. By this we mean, that if an electrical circuit is the initial high-dimensional pH system, we want the reduced order model to be still interpretable as an electronic circuit. In the case of the well-known mass spring damper (MSD) system, there are MOR methods available, which already guarantee the preservation of this particular structure. Moreover, we show that our new structure-preserving MOR method, which is based on symplectic MOR methods, will recover the known second-order Arnoldi method in the case of MSD systems. However, for the example of an electrical circuit pH model (and more models of similar block structure), our method yields a novel model reduction method. We present numerical results on the aforementioned electronic circuit model, highlighting the advantages of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_07751 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Symplectic model order reduction of port-Hamiltonian systems Glas, Silke Mamunuzzaman, Mir Mu, Hongliang Zwart, Hans Optimization and Control Classical Analysis and ODEs 34C20, 65P10, 70H33, 93B10, 93B1, 93C05 This work proposes a novel structure-preserving model order reduction (MOR) method for linear, time-invariant port-Hamiltonian (pH) systems. Our goal is to construct a reduced order pH system, which can still be interpreted in the physical domain of the full order model. By this we mean, that if an electrical circuit is the initial high-dimensional pH system, we want the reduced order model to be still interpretable as an electronic circuit. In the case of the well-known mass spring damper (MSD) system, there are MOR methods available, which already guarantee the preservation of this particular structure. Moreover, we show that our new structure-preserving MOR method, which is based on symplectic MOR methods, will recover the known second-order Arnoldi method in the case of MSD systems. However, for the example of an electrical circuit pH model (and more models of similar block structure), our method yields a novel model reduction method. We present numerical results on the aforementioned electronic circuit model, highlighting the advantages of the proposed method. |
| title | Symplectic model order reduction of port-Hamiltonian systems |
| topic | Optimization and Control Classical Analysis and ODEs 34C20, 65P10, 70H33, 93B10, 93B1, 93C05 |
| url | https://arxiv.org/abs/2203.07751 |