State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle

This study presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state-space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilin...

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Bibliographic Details
Published in:IET control theory & applications Vol. 12; no. 12; pp. 1704 - 1713
Main Authors: Zhang, Xiao, Ding, Feng, Xu, Ling, Yang, Erfu
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 14.08.2018
Subjects:
bilinear state observer
bilinear system
bilinear systems
BSO‐based forgetting factor recursive least squares algorithm
BSO‐RLS algorithm
combined parameter
decomposition–coordination principle
extremum principle
filtering theory
gradient methods
hierarchical identification principle
hierarchical least squares algorithm
identification
Kalman filter
Kalman filters
least squares approximations
linear systems
observer canonical state‐space model
observers
parameter estimation
parameter tracking capability
recursive estimation
Research Article
squares parameter estimation
state estimation
state filter
state‐space methods
BSO-based forgetting factor recursive least squares algorithm
Kalman filter
hierarchical least squares algorithm
combined parameter
parameter tracking capability
state filter
extremum principle
identification
bilinear system
recursive estimation
parameter estimation
Kalman filters
gradient methods
decomposition–coordination principle
observer canonical state-space model
least squares approximations
filtering theory
bilinear systems
linear systems
squares parameter estimation
hierarchical identification principle
state estimation
bilinear state observer
BSO-RLS algorithm
observers
state-space methods
ISSN:1751-8644, 1751-8652
Online Access:Get full text
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Summary:This study presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state-space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO-based recursive least squares (BSO-RLS) algorithm is developed. For comparison with the BSO-RLS algorithm, by dividing the system into three fictitious subsystems on the basis of the decomposition–coordination principle, a BSO-based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO-based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.
ISSN:1751-8644
1751-8652
DOI:10.1049/iet-cta.2018.0156