Geodesic
Data transformation technique in the data informativity approach via algebraic sequences
Kybernetika, Tome 60 (2024) no. 2, pp. 228-243 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The data-informativity approach in data-driven control focuses on data and their matching model sets for system design and analysis. The approach offers a new mathematical formulation different from model-based control and is expected to progress. In model-based control, the introduction of equivalent transformations has made system analysis and design easier and facilitated theoretical development. In this study, we focus on data transformations and their transformation of matching model sets. We first introduce an algebraic sequence representing the relationship between the data and model set, and using this algebraic approach, we utilize propositions from homology theory, such as kernel universality, to analyze data and model transformations. This technique is significant not only mathematically but also in engineering. Further, we demonstrate how this technique can be applied to derive controllability judgments for data informativity-based analysis. Finally, we prove that design problems can be reduced to analysis problems involving controller inclusion.
The data-informativity approach in data-driven control focuses on data and their matching model sets for system design and analysis. The approach offers a new mathematical formulation different from model-based control and is expected to progress. In model-based control, the introduction of equivalent transformations has made system analysis and design easier and facilitated theoretical development. In this study, we focus on data transformations and their transformation of matching model sets. We first introduce an algebraic sequence representing the relationship between the data and model set, and using this algebraic approach, we utilize propositions from homology theory, such as kernel universality, to analyze data and model transformations. This technique is significant not only mathematically but also in engineering. Further, we demonstrate how this technique can be applied to derive controllability judgments for data informativity-based analysis. Finally, we prove that design problems can be reduced to analysis problems involving controller inclusion.
DOI : 10.14736/kyb-2024-2-0228
Classification : 15A06, 93A99
Keywords: data-driven control; data informativity-based analysis; analysis and design problems; algebraic sequence; homology theory 
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Tanaka, Yuki; Kaneko, Osamu. Data transformation technique in the data informativity approach via algebraic sequences. Kybernetika, Tome 60 (2024) no. 2, pp. 228-243. doi: 10.14736/kyb-2024-2-0228

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