A new kernel-based approach for overparameterized Hammerstein system identification

TL;DR

This paper introduces a novel kernel-based identification method for Hammerstein systems, effectively estimating both the linear dynamic component and the static nonlinearity with improved accuracy and stability.

Contribution

The paper presents a new regularized kernel approach tailored for Hammerstein system identification, enabling unique decomposition of the overparameterized vector into system components.

Findings

Method outperforms standard techniques in numerical experiments.

Kernel approach reduces variance in estimates.

Provides a stable and unique decomposition of system parameters.

Abstract

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of $p$ basis functions. We reconstruct the $p$ coefficients of the nonlinearity together with the first $n$ samples of the impulse response of the linear system by estimating an $np$-dimensional overparameterized vector, which contains all the combinations of the unknown variables. To avoid high variance in these estimates, we adopt a regularized kernel-based approach and, in particular, we introduce a new kernel tailored for Hammerstein system identification. We show that the resulting scheme provides an estimate of the overparameterized vector that can be uniquely decomposed as the combination of an impulse response and $p$ coefficients of the static nonlinearity. We also show, through several numerical experiments, that the proposed method compares very favorably with two standard methods for Hammerstein system identification.