Predictor-Based Tensor Regression (PBTR) for LPV subspace identification

Predictor-Based Tensor Regression (PBTR) for LPV subspace identification

Gunes, Bilal (TU Delft Team Jan-Willem van Wingerden)
van Wingerden, J.W. (TU Delft Team Jan-Willem van Wingerden)
Verhaegen, M.H.G. (TU Delft Team Raf Van de Plas)

2017

The major bottleneck in state-of-the-art Linear Parameter Varying (LPV) subspace methods is the curse-of-dimensionality during the first regression step. In this paper, the origin of the curse-of-dimensionality is pinpointed and subsequently a novel method is proposed which does not suffer from this bottleneck. The problem is related to the LPV sub-Markov parameters. These have inherent structure and are dependent on each other. But state-of-the-art LPV subspace methods parametrize the LPV sub-Markov parameters independently. This means the inherent structure is not preserved in the parametrization. In turn this leads to a superfluous parametrization with the curse-of-dimensionality. The solution lies in using parametrizations which preserve the inherent structure sufficiently to avoid the curse-of-dimensionality. In this paper a novel method based on tensor regression is proposed. This novel method is named the Predictor-Based Tensor Regression method (PBTR). This method preserves the inherent structure sufficiently to avoid the curse-of-dimensionality. Simulation results show that PBTR has superior performance with respect to both state-of-the-art LPV subspace techniques and also non-convex techniques.

Closed-loop identification
Identification
LPV systems
Subspace methods
Tensor regression

http://resolver.tudelft.nl/uuid:d8f9074b-b18f-4e89-a8c0-807c8d14da12

https://doi.org/10.1016/j.automatica.2017.01.039

2019-03-06

0005-1098

Automatica, 79, 235-243

Accepted Author Manuscript

Institutional Repository

journal article

© 2017 Bilal Gunes, J.W. van Wingerden, M.H.G. Verhaegen