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

TL;DR

This paper introduces a new data-driven control framework specifically designed for T-product-based dynamical systems, enabling system identification and stabilization directly from data without explicit model identification.

Contribution

It develops necessary and sufficient conditions for data informativity, stabilization, and regulation of TPDSs, addressing a gap in control methods for multi-linear tensor systems.

Findings

Established conditions for data informativity in TPDSs

Provided methods for stabilization via state feedback

Validated the approach with numerical examples

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.