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

doi:10.1016/j.automatica.2017.01.039

2017-05-01

Bilal Gunes *

Jan‐Willem van Wingerden

Michel Verhaegen

DOI：10.1016/j.automatica.2017.01.039

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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. (C) 2017 Elsevier Ltd. All rights reserved.

Keyword:

Identification

Subspace methods

Closed-loop identification

LPV systems

Tensor regression