Tensor nuclear norm LPV subspace identification

Linear Parameter Varying (LPV) subspace identification methods suffer from an exponential growth in number of parameters to estimate. This results in problems with ill-conditioning. In literature, attempts have been made to address the ill-conditioning by using regularization. Its effectiveness hinges on suitable a priori knowledge. In this paper we propose using a novel, alternative regularization. That is, we first show that the LPV sub-Markov parameters can be organized into several tensors which are multi-linear low-rank by construction. Namely, their matricization along any mode is a low-rank matrix. Then we propose a novel convex method with tensor nuclear norm regularization which exploits this low-rank property. Simulation results show that the novel method can have higher performance than the regularized LPV-PBSIDopt technique in terms of variance accounted for.