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

TL;DR

This paper introduces a new tensor-based framework for analyzing T-product dynamical systems, preserving higher-order data structures and improving computational efficiency in system identification and stability analysis.

Contribution

It presents a novel approach for data-driven analysis of TPDSs that maintains tensor structure and enhances computational performance over traditional methods.

Findings

Effective system identification using the T-product framework

Improved stability and controllability analysis for TPDSs

Numerical examples demonstrate computational advantages

Abstract

A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven frameworks are not naturally equipped to process tensors without first unfolding or flattening the data, which can result in a loss of crucial higher-order structural information. In this article, we introduce a novel framework for the data-driven analysis 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 examine the data informativity of TPDSs concerning system identification, stability, controllability, and stabilizability and illustrate significant computational improvements over traditional approaches by leveraging the unique properties of the T-product. The effectiveness of our framework is demonstrated through numerical examples.