Data-driven Control of T-Product-based Dynamical Systems

Fuente: arXiv
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Main Authors: He, Ziqin, Mei, Yidan, Mei, Shenghan, Mao, Xin, Dong, Anqi, Wang, Ren, Chen, Can
Format: Preprint
Published: 2025
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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