Multilinear state space system identification with matrix product operators

Abstract In this article, we introduce a matrix product operator, also called tensor train matrix, representation of discrete-time multilinear state space models and develop a corresponding system identification method. Using matrix product operators allows us to store the exponential number of model coefficients with a linear storage complexity. The derived system identification algorithm estimates the matrix product operator of the multilinear state space model directly from the measured data. This results in lower computational complexity compared to traditional nonlinear optimization methods. The effectiveness of our proposed model and method is demonstrated by a numerical experiment, where the identification of a degree-16 multilinear state space system in MATLAB on a standard desktop computer takes about 8 minutes with a relative validation error of 0.003%.