Hierarchical gradient‐ and least‐squares‐based iterative estimation algorithms for input‐nonlinear output‐error systems from measurement information by using the over‐parameterization

• Published in: International journal of robust and nonlinear control Vol. 34; no. 2; pp. 1120 - 1147
• Main Authors: Ding, Feng, Xu, Ling, Zhang, Xiao, Ma, Hao
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.01.2024
• Subjects: auxiliary model; Error analysis; hierarchical identification; Iterative algorithms; Iterative methods; least squares; Mathematical models; nonlinear system; over‐parameterization; Parameter identification; Parameterization; Stochastic systems; System effectiveness
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7014

This article investigates the parameter identification problems of the stochastic systems described by the input‐nonlinear output‐error (IN‐OE) model. This IN‐OE model consists of two submodels, one is an input nonlinear model and the other is a linear output‐error model. The difficulty in the parameter identification of the IN‐OE model is that the information vector contains the unknown variables, which are the noise‐free (true) outputs of the system, the approach taken here is to replace the unknown terms with the outputs of the auxiliary model. Based on the over‐parameterization model and the hierarchical identification principle, an over‐parameterization auxiliary model hierarchical gradient‐based iterative algorithm and an over‐parameterization auxiliary model hierarchical least‐squares‐based iterative algorithm are proposed to estimate the unknown parameters of the IN‐OE systems. Finally, two numerical simulation examples are given to demonstrate the effectiveness of the proposed algorithms.