One Equation to Rule Them All -- Part II: Direct Data-Driven Reduction and Regulation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915460452188160 |
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| author | Mao, Junyu Williams, Emyr Mylvaganam, Thulasi Scarciotti, Giordano |
| author_facet | Mao, Junyu Williams, Emyr Mylvaganam, Thulasi Scarciotti, Giordano |
| contents | The Sylvester equation underpins a wide spectrum of control synthesis and systems analysis tools associated with cascade interconnections. In the preceding Part I [1] of this article, it was shown that such an equation can be reformulated using data, enabling the production of a collection of data-driven stabilisation procedures. In this second part of the article, we continue to develop the framework established in Part I to solve two important control-theoretic problems: model order reduction and output regulation. For the model order reduction problem we provide a solution from input-state measurements, from input-output measurements, and we study the effect of the noise. For the output regulation problem, we provide data-driven solutions for the static and dynamic feedback problem. The proposed designs are illustrated by means of examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One Equation to Rule Them All -- Part II: Direct Data-Driven Reduction and Regulation Mao, Junyu Williams, Emyr Mylvaganam, Thulasi Scarciotti, Giordano Systems and Control Optimization and Control The Sylvester equation underpins a wide spectrum of control synthesis and systems analysis tools associated with cascade interconnections. In the preceding Part I [1] of this article, it was shown that such an equation can be reformulated using data, enabling the production of a collection of data-driven stabilisation procedures. In this second part of the article, we continue to develop the framework established in Part I to solve two important control-theoretic problems: model order reduction and output regulation. For the model order reduction problem we provide a solution from input-state measurements, from input-output measurements, and we study the effect of the noise. For the output regulation problem, we provide data-driven solutions for the static and dynamic feedback problem. The proposed designs are illustrated by means of examples. |
| title | One Equation to Rule Them All -- Part II: Direct Data-Driven Reduction and Regulation |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2508.17251 |