Data-driven Analysis of Multi-linear Dynamical Systems through Tensor Decompositions
Ziqian He, Yidan Mei, Shenghan Mei, Can Chen · 2025
In our recent article [Chen et al., SIAM J Control Optim], we introduced a system-theoretic approach to a class of discrete-time multi-linear time-invariant (MLTI) dynamical systems, where the states, inputs, and outputs are all tensors. The purpose of this article is to delve into the role of data for MLTI systems. We perform data-driven analysis, concerning system identification, stability, controllability, and stabilizability, of MLTI systems. In particular, we exploit advanced tensor decomposition techniques encompassing CANDECOMP/PARAFAC decomposition and tensor train decomposition to establish effective criteria for determining the data informativity for the aforementioned system properties. We further demonstrate our framework with numerical examples.