Data-driven Control of T-Product-based Dynamical Systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909503037898752 |
|---|---|
| author | He, Ziqin Mei, Yidan Mei, Shenghan Mao, Xin Dong, Anqi Wang, Ren Chen, Can |
| author_facet | He, Ziqin Mei, Yidan Mei, Shenghan Mao, Xin Dong, Anqi Wang, Ren Chen, Can |
| contents | Data-driven control is a powerful tool that enables the design and implementation of control strategies directly from data without explicitly identifying the underlying system dynamics. While various data-driven control techniques, such as stabilization, linear quadratic regulation, and model predictive control, have been extensively developed, these methods are not inherently suited for multi-linear dynamical systems, where the states are represented as higher-order tensors. In this article, we propose a novel framework for data-driven control 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 offer necessary and sufficient conditions to determine the data informativity for system identification, stabilization by state feedback, and T-product quadratic regulation of TPDSs with detailed complexity analyses. Finally, we validate our framework through numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14591 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-driven Control of T-Product-based Dynamical Systems He, Ziqin Mei, Yidan Mei, Shenghan Mao, Xin Dong, Anqi Wang, Ren Chen, Can Systems and Control 37N35, 93-08, 93A15 Data-driven control is a powerful tool that enables the design and implementation of control strategies directly from data without explicitly identifying the underlying system dynamics. While various data-driven control techniques, such as stabilization, linear quadratic regulation, and model predictive control, have been extensively developed, these methods are not inherently suited for multi-linear dynamical systems, where the states are represented as higher-order tensors. In this article, we propose a novel framework for data-driven control 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 offer necessary and sufficient conditions to determine the data informativity for system identification, stabilization by state feedback, and T-product quadratic regulation of TPDSs with detailed complexity analyses. Finally, we validate our framework through numerical examples. |
| title | Data-driven Control of T-Product-based Dynamical Systems |
| topic | Systems and Control 37N35, 93-08, 93A15 |
| url | https://arxiv.org/abs/2502.14591 |