Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

This article deals with the problems of the parameter estimation for feedback nonlinear controlled autoregressive systems (i.e., feedback nonlinear equation‐error systems). The bilinear‐in‐parameter identification model is formulated to describe the feedback nonlinear system. An overall recursive le...

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Bibliographic Details
Published in:International journal of robust and nonlinear control Vol. 32; no. 9; pp. 5534 - 5554
Main Authors: Wei, Chun, Zhang, Xiao, Xu, Ling, Ding, Feng, Yang, Erfu
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 01.06.2022
Subjects:
Algorithms
bilinear‐in‐parameter model
Control systems
Convergence
convergence analysis
Feedback
feedback nonlinear system
gradient search
Least squares
Nonlinear control
Nonlinear equations
Nonlinear systems
Parameter estimation
Parameter identification
Stochastic processes
ISSN:1049-8923, 1099-1239
Online Access:Get full text
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Summary:This article deals with the problems of the parameter estimation for feedback nonlinear controlled autoregressive systems (i.e., feedback nonlinear equation‐error systems). The bilinear‐in‐parameter identification model is formulated to describe the feedback nonlinear system. An overall recursive least squares algorithm is developed to handle the difficulty of the bilinear‐in‐parameter. For the purpose of avoiding the heavy computational burden, an overall stochastic gradient algorithm is deduced and the forgetting factor is introduced to improve the convergence rate. Furthermore, the convergence analysis of the proposed algorithms are established by means of the stochastic process theory. The effectiveness of the proposed algorithms are illustrated by the simulation example.
Bibliography:Funding information
National Natural Science Foundation of China, No. 61873111 and the 111 Project (B12018)
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ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.6101