IEEE Transactions on Automatic Control, Vol.63, No.11, 3897-3903, 2018
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 that are multilinear 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.