Two-stage identification of continuous-time Hammerstein systems using Gaussian process models

Abstract

This paper deals with a two-stage identification of continuous-time Hammerstein systems using a Gaussian process (GP) model. The Hammerstein system is described by the cascade connection of a nonlinear static part followed by a linear dynamic part. In the first stage, the nonlinear static part represented by the GP model is estimated based on multiple sets of data of constant input and corresponding steady-state output. Then, in the second stage, the linear dynamic part is estimated by the linear least-squares method based on the approximated discrete-time estimation model derived by a digital pre-filter. Since the training of the GP model is limited to estimating the nonlinear static part only, the proposed method can be applied to systems whose linear dynamic parts have arbitrary order and can significantly reduce the computational burden. The effectiveness of the proposed method is confirmed through numerical experiments.