Kernelized identification of linear parameter-varying models with linear fractional representation

The article presents a method for the identification of Linear Parameter-Varying (LPV) models in a Linear Fractional Representation (LFR), which corresponds to a Linear Time-Invariant (LTI) model connected to a scheduling variable dependency via a feedback path. A two-stage identification approach is proposed. In the first stage, Kernelized Canonical Correlation Analysis (KCCA) is formulated to estimate the state sequence of the underlying LPV model. In the second stage, a non-linear least squares cost function is minimized by employing a coordinate descent algorithm to estimate latent variables characterizing the LFR and the unknown model matrices of the LTI block by using the state estimates obtained at the first stage. Here, it is assumed that the structure of the scheduling variable dependent block in the feedback path is fixed. For a special case of affine dependence of the model on the feedback block, it is shown that the optimization problem in the second stage reduces to ordinary least-squares followed by a singular value decomposition.