TY - JOUR
T1 - Tensor nuclear norm LPV subspace identification
AU - Gunes, Bilal
AU - van Wingerden, Jan Willem
AU - Verhaegen, Michel
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Closed-loop identification
KW - Identification
KW - LPV systems
KW - Subspace Methods
KW - Tensor regression
UR - http://www.scopus.com/inward/record.url?scp=85041425540&partnerID=8YFLogxK
U2 - 10.1109/TAC.2018.2800772
DO - 10.1109/TAC.2018.2800772
M3 - Article
AN - SCOPUS:85041425540
SN - 0018-9286
VL - 63
SP - 3897
EP - 3903
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 11
ER -