Adaptive Kernel Canonical Correlation Analysis Algorithms for Nonparametric Identification Of Wiener and Hammerstein Systems

This paper treats the identification of non-linear systems that consist of a cascade of a linear channel and a nonlinearity, such as the well-known Wiener and Hammerstein systems. In particular, the authors follow a supervised identification approach that simultaneously identifies both parts of the nonlinear system. Given the correct restrictions on the identification problem, they show how Kernel Canonical Correlation Analysis (KCCA) emerges as the logical solution to this problem. They, then extend the proposed identification algorithm to an adaptive version allowing to deal with time-varying systems. In order to avoid over-fitting problems, they discuss and compare three possible regularization techniques for both the batch and the adaptive versions of the proposed algorithm. Simulations are included to demonstrate the effectiveness of the presented algorithm.