Least-squares-based iterative identification algorithm for Hammerstein nonlinear systems with non-uniform sampling

Abstract

This paper focuses on identification problems for Hammerstein systems with non-uniform sampling. By using the over-parameterization technique, we derive a linear regressive identification model with different input updating rates. To solve the identification problem of Hammerstein output error systems with the unmeasurable variables in the information vector, the least-squares-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. The performances of the proposed algorithm are analysed and compared by using a numerical example.

Least-Squares-Based Iterative Identification Algorithm for Wiener Nonlinear Systems

“…The simulation results verified the effectiveness of the proposed algorithm. The proposed method for Wiener nonlinear systems can combine the auxiliary model identification idea [33][34][35][36][37], the multi-innovation identification theory [38][39][40][41][42][43][44], the bias compensation methods [45][46][47][48], and the maximum likelihood principle [49][50][51][52] to study identification problems of linear or nonlinear systems with colored noise and Hammerstein nonlinear systems [53][54][55][56][57][58][59].…”

Recursive Least-Squares Estimation for Hammerstein Nonlinear Systems with Nonuniform Sampling

“…𝛽 𝑖 (𝑧) 𝑢 (𝑘𝑇 + 𝑡 𝑖−1 ) . (10) Substituting ( 10) into (7), the system output 𝑦 1 (𝑘𝑇) can be expressed as…”

“…For example, Chen et al studied identification problems for the Hammerstein systems with saturation and dead-zone nonlinearities by choosing an appropriate switching function [8]; Ding et al presented the projection, the stochastic gradient, and the Newton recursive and the Newton iterative identification algorithms for the Hammerstein nonlinear systems, and then they analyzed and compared the performances of these approaches by numerical examples [9]. Li et al derived a least-squares based iterative algorithm for the Hammerstein output error systems with nonuniform sampling by using the overparameterization model [10].…”

Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems

“…Due to the complexity of arbitrary non-uniform sampling, most of the literature works have focused on periodically non-uniformly sampled-data systems [30,31]. For periodically non-uniformly sampled-data Hammerstein systems, Li et al derived the lifted transfer function model by means of the lifting technique and presented a least squares-based iterative algorithm for parameter estimation [32]. The lifting technique is a benchmark tool to deal with multirate and non-uniformly sampled-data systems [33,34].…”