Tensor network subspace identification of polynomial state space models

This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus avoiding the curse of dimensionality. We also prove how the block Hankel data matrices in the subspace method can be exactly represented by low rank tensor networks, reducing the computational and storage complexity significantly. The performance and accuracy of our subspace identification algorithm are illustrated by experiments, showing that our tensor network implementation identifies a seventh degree polynomial state space model around 20 times faster than the standard matrix implementation before the latter fails due to insufficient memory. The proposed algorithm is also robust with respect to noise and therefore applicable to practical systems.