Data-driven Control of T-Product-based Dynamical Systems
Ziqin He, Yidan Mei, Shenghan Mei, Xin Mao, Anqi Dong, Ren Wang, Can Chen
TL;DR
The paper addresses data-driven control for T-product-based dynamical systems (TPDSs), where states and dynamics are third-order tensors linked by a T-product. It develops necessary and sufficient data informativity conditions for system identification, stabilization by state feedback, and T-product quadratic regulation (TQR), leveraging Fourier-domain decoupling to achieve computational efficiency. The framework reduces complex tensor problems to per-slice matrix conditions and explores substantial time savings over unfolding-based methods, backed by numerical examples on stabilization and TQR. The results enable scalable, tensor-structured control design for high-dimensional data such as images and videos, with future directions including real-data applications and extensions to MPC and nonlinear/hybrid TPDSs.
Abstract
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.