Incorporating Fixed-Pole Information in the Data-Driven Least Squares Realization Problem
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908933981995008 |
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| author | Vermeersch, Christof Lagauw, Sibren De Moor, Bart |
| author_facet | Vermeersch, Christof Lagauw, Sibren De Moor, Bart |
| contents | In practical least squares realization problems, partial information about the pole locations of the dynamical model may be known a priori. Existing techniques for incorporating this prior knowledge, such as prefiltering the given data, are typically heuristic and lack theoretical guarantees. We extend our previously developed globally optimal estimation approach to accommodate fixed poles in the least squares realization problem. In particular, we reformulate the problem as a (rectangular) multiparameter eigenvalue problem, the eigenvalues of which characterize all local and global minimizers of the constrained estimation problem. We present numerical examples to demonstrate the effectiveness of the proposed method and experimentally validate the paper's central hypothesis: incorporating a priori information on the poles enhances the estimation results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incorporating Fixed-Pole Information in the Data-Driven Least Squares Realization Problem Vermeersch, Christof Lagauw, Sibren De Moor, Bart Optimization and Control In practical least squares realization problems, partial information about the pole locations of the dynamical model may be known a priori. Existing techniques for incorporating this prior knowledge, such as prefiltering the given data, are typically heuristic and lack theoretical guarantees. We extend our previously developed globally optimal estimation approach to accommodate fixed poles in the least squares realization problem. In particular, we reformulate the problem as a (rectangular) multiparameter eigenvalue problem, the eigenvalues of which characterize all local and global minimizers of the constrained estimation problem. We present numerical examples to demonstrate the effectiveness of the proposed method and experimentally validate the paper's central hypothesis: incorporating a priori information on the poles enhances the estimation results. |
| title | Incorporating Fixed-Pole Information in the Data-Driven Least Squares Realization Problem |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.09394 |