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

Voir la notice de l'article

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 
@article{10_14736_kyb_2024_2_0228,
     author = {Tanaka, Yuki and Kaneko, Osamu},
     title = {Data transformation technique in the data informativity approach via algebraic sequences},
     journal = {Kybernetika},
     pages = {228--243},
     year = {2024},
     volume = {60},
     number = {2},
     doi = {10.14736/kyb-2024-2-0228},
     mrnumber = {4757771},
     zbl = {07893456},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-2-0228/}
}
TY  - JOUR
AU  - Tanaka, Yuki
AU  - Kaneko, Osamu
TI  - Data transformation technique in the data informativity approach via algebraic sequences
JO  - Kybernetika
PY  - 2024
SP  - 228
EP  - 243
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-2-0228/
DO  - 10.14736/kyb-2024-2-0228
LA  - en
ID  - 10_14736_kyb_2024_2_0228
ER  - 
%0 Journal Article
%A Tanaka, Yuki
%A Kaneko, Osamu
%T Data transformation technique in the data informativity approach via algebraic sequences
%J Kybernetika
%D 2024
%P 228-243
%V 60
%N 2
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-2-0228/
%R 10.14736/kyb-2024-2-0228
%G en
%F 10_14736_kyb_2024_2_0228
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

[1] Atiyah, M.: Introduction to Commutative Algebra. CRC Press, 2023. | MR

[2] Eising, J., Trentelman, H. L., Camlibel, M. K.: Data informativity for observability: an invariance-based approach. In: 2020 European Control Conference (ECC), IEEE 2020, pp. 1057-1059. | DOI | MR

[3] Hjalmarsson, H., Gunnarsson, S., Gevers, M.: A convergent iterative restricted complexity control design scheme. In: Proc. 1994 33rd IEEE Conference on Decision and Control, Vol. 2, IEEE 1994, pp. 1735-1740. | DOI

[4] Hou, Z. S., Wang, Z.: From model-based control to data-driven control: Survey, classification and perspective. Inform. Sci. 235 (2013), 3-35. | DOI | MR

[5] Leinster, T.: Basic Category Theory. Cambridge University Press 143 (2014). | DOI | MR

[6] Ljung, L.: System identification. Signal Analysis Prediction, Springer 1998, pp. 163-173.

[7] Persis, C. De, Tesi, P.: Formulas for data-driven control: Stabilization, optimality, and robustness. IEEE Trans. Automat. Control 65 (2019), 3, 909-924. | DOI | MR

[8] Saito, T.: The World of Linear Algebra. University of Tokyo Press, 2007.

[9] Soma, S., Kaneko, O., Fujii, T.: A new method of controller parameter tuning based on input-output data-Fictitious Reference Iterative Tuning (FRIT)-. IFAC Proc. Vol. 37 (2004), 12, 789-794. | DOI

[10] Swanson, I.: Homological Algebra. Fall, Graz 2018.

[11] Tanaka, Y., Kaneko, O., Sueyoshi, T-: Data-driven control synthesis for dissipative systems by using input-output data via algebraic approach. In: Proc. SICE Annual Conference 2023, pp. 1462-1466.

[12] Tanaka, Y., Kaneko, O.: Equivalent transformations in the data-informativity framework and its applications: homological algebraic approach. In: 23rd International Conference on Control, Automation and Systems (ICCAS), IEEE 2023, pp. 60-65. | DOI

[13] Waarde, H. J. Van, Eising, J., Trentelman, H. L., Camlibel, M. K.: Data informativity: a new perspective on data-driven analysis and control. IEEE Trans. Automat. Control 65 (2020), 11, 4753-4768. | DOI | MR

[14] Waarde, H. J. Van, Camlibel, M. K.: From noisy data to feedback controllers: Nonconservative design via a matrix S-lemma. IEEE Trans. Automat. Control 67 (2020), 1, 162-175. | DOI | MR

[15] Waarde, H. J. Van, Camlibel, M. K.: A matrix Finsler's lemma with applications to data-driven control. In: 60th IEEE Conference on Decision and Control (CDC), IEEE 2021, pp. 5777-5782. | DOI | MR

[16] Waarde, H. J. Van, Camlibel, M. K., Rapisarda, P., Trentelman, H. L.: Data-driven dissipativity analysis: application of the matrix S-lemma. IEEE Control Systems Mag. 42 (2022), 3, 140-149. | DOI | MR

[17] Waarde, H. J. Van, Eising, J., Camlibel, M. K., Trentelman, H. L.: A behavioral approach to data-driven control with noisy input-output data. IEEE Trans. Automat. Control (2023). | DOI | MR

[18] Waarde, H. J. Van, Eising, J., Camlibel, M. K., Trentelman, H. L.: The informativity approach: to data-driven analysis and control. IEEE Control Systems Magazine 43 (2023), 6, 32-66. | DOI | MR

[19] Willems, J. C., Rapisarda, P., Markovsky, I., Moor, B. L. De: A note on persistency of excitation. Systems Control Lett. 54 (2005), 4, 325-329. | DOI | MR

Cité par Sources :