Convergence Analysis of the Hierarchical Least Squares Algorithm for Bilinear-in-Parameter Systems

Xuehai Wang; Feng Ding; Fuad E. Alsaadi; Tasawar Hayat

doi:10.1007/s00034-016-0278-7

Convergence Analysis of the Hierarchical Least Squares Algorithm for Bilinear-in-Parameter Systems

Xuehai Wang
, Feng Ding
, Fuad E. Alsaadi
, Tasawar Hayat

Jiangnan University
Henan University of Urban Construction
Faculty of Engineering, King Abdulaziz University
Quaid-I-Azam University

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

This paper studies the convergence of the hierarchical identification algorithm for bilinear-in-parameter systems. By replacing the unknown variables in the information vector with their estimates, a hierarchical least squares algorithm is derived based on the model decomposition. The proposed algorithm has higher computational efficiency than the over-parameterization model-based recursive least squares algorithm. The performance analysis shows that the parameter estimation errors converge to zero under persistent excitation conditions. The effectiveness of the proposed algorithm is verified by simulation examples.

Original language	English
Pages (from-to)	4307-4330
Number of pages	24
Journal	Circuits, Systems, and Signal Processing
Volume	35
Issue number	12
DOIs	https://doi.org/10.1007/s00034-016-0278-7
State	Published - 1 Dec 2016
Externally published	Yes

Keywords

Least squares
Martingale convergence theorem
Nonlinear system
Parameter estimation
Recursive identification

Access to Document

10.1007/s00034-016-0278-7

Cite this

@article{a65ed215e885416f8005c144ce54347a,

title = "Convergence Analysis of the Hierarchical Least Squares Algorithm for Bilinear-in-Parameter Systems",

abstract = "This paper studies the convergence of the hierarchical identification algorithm for bilinear-in-parameter systems. By replacing the unknown variables in the information vector with their estimates, a hierarchical least squares algorithm is derived based on the model decomposition. The proposed algorithm has higher computational efficiency than the over-parameterization model-based recursive least squares algorithm. The performance analysis shows that the parameter estimation errors converge to zero under persistent excitation conditions. The effectiveness of the proposed algorithm is verified by simulation examples.",

keywords = "Least squares, Martingale convergence theorem, Nonlinear system, Parameter estimation, Recursive identification",

author = "Xuehai Wang and Feng Ding and Alsaadi, \{Fuad E.\} and Tasawar Hayat",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2016",

month = dec,

day = "1",

doi = "10.1007/s00034-016-0278-7",

language = "English",

volume = "35",

pages = "4307--4330",

journal = "Circuits, Systems, and Signal Processing",

issn = "0278-081X",

publisher = "Springer Nature",

number = "12",

}

TY - JOUR

T1 - Convergence Analysis of the Hierarchical Least Squares Algorithm for Bilinear-in-Parameter Systems

AU - Wang, Xuehai

AU - Ding, Feng

AU - Alsaadi, Fuad E.

AU - Hayat, Tasawar

PY - 2016/12/1

Y1 - 2016/12/1

N2 - This paper studies the convergence of the hierarchical identification algorithm for bilinear-in-parameter systems. By replacing the unknown variables in the information vector with their estimates, a hierarchical least squares algorithm is derived based on the model decomposition. The proposed algorithm has higher computational efficiency than the over-parameterization model-based recursive least squares algorithm. The performance analysis shows that the parameter estimation errors converge to zero under persistent excitation conditions. The effectiveness of the proposed algorithm is verified by simulation examples.

AB - This paper studies the convergence of the hierarchical identification algorithm for bilinear-in-parameter systems. By replacing the unknown variables in the information vector with their estimates, a hierarchical least squares algorithm is derived based on the model decomposition. The proposed algorithm has higher computational efficiency than the over-parameterization model-based recursive least squares algorithm. The performance analysis shows that the parameter estimation errors converge to zero under persistent excitation conditions. The effectiveness of the proposed algorithm is verified by simulation examples.

KW - Least squares

KW - Martingale convergence theorem

KW - Nonlinear system

KW - Parameter estimation

KW - Recursive identification

UR - https://www.scopus.com/pages/publications/84988448062

U2 - 10.1007/s00034-016-0278-7

DO - 10.1007/s00034-016-0278-7

M3 - Article

AN - SCOPUS:84988448062

SN - 0278-081X

VL - 35

SP - 4307

EP - 4330

JO - Circuits, Systems, and Signal Processing

JF - Circuits, Systems, and Signal Processing

IS - 12

ER -

Convergence Analysis of the Hierarchical Least Squares Algorithm for Bilinear-in-Parameter Systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this