Data-driven Analysis of T-Product-based Dynamical Systems
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916456771354624 |
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| author | Mao, Xin Dong, Anqi He, Ziqin Mei, Yidan Chen, Can |
| author_facet | Mao, Xin Dong, Anqi He, Ziqin Mei, Yidan Chen, Can |
| contents | A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven frameworks are not naturally equipped to process tensors without first unfolding or flattening the data, which can result in a loss of crucial higher-order structural information. In this article, we introduce a novel framework for the data-driven analysis of T-product-based dynamical systems (TPDSs), where the system evolution is governed by the T-product between a third-order dynamic tensor and a third-order state tensor. In particular, we examine the data informativity of TPDSs concerning system identification, stability, controllability, and stabilizability and illustrate significant computational improvements over traditional approaches by leveraging the unique properties of the T-product. The effectiveness of our framework is demonstrated through numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven Analysis of T-Product-based Dynamical Systems Mao, Xin Dong, Anqi He, Ziqin Mei, Yidan Chen, Can Systems and Control Dynamical Systems Optimization and Control 15A69, 93B30, 93C10, 93Bxx A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven frameworks are not naturally equipped to process tensors without first unfolding or flattening the data, which can result in a loss of crucial higher-order structural information. In this article, we introduce a novel framework for the data-driven analysis of T-product-based dynamical systems (TPDSs), where the system evolution is governed by the T-product between a third-order dynamic tensor and a third-order state tensor. In particular, we examine the data informativity of TPDSs concerning system identification, stability, controllability, and stabilizability and illustrate significant computational improvements over traditional approaches by leveraging the unique properties of the T-product. The effectiveness of our framework is demonstrated through numerical examples. |
| title | Data-driven Analysis of T-Product-based Dynamical Systems |
| topic | Systems and Control Dynamical Systems Optimization and Control 15A69, 93B30, 93C10, 93Bxx |
| url | https://arxiv.org/abs/2410.20541 |