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Research Papers

Iterative Identification of Discrete-Time Systems With Bilinear Forms in the Presence of Colored Noises Based on the Hierarchical Principle

[+] Author and Article Information
Mengting Chen

Key Laboratory of Advanced Process Control for
Light Industry (Ministry of Education),
Jiangnan University,
Wuxi 214122, China
e-mail: mtchen11@126.com

Feng Ding

Key Laboratory of Advanced Process Control for
Light Industry (Ministry of Education),
Jiangnan University,
Wuxi 214122, China;
College of Automation and
Electronic Engineering,
Qingdao University of
Science and Technology,
Qingdao 266061, China;
Department of Mathematics,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: fding@jiangnan.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 11, 2018; final manuscript received May 30, 2019; published online July 15, 2019. Assoc. Editor: Bernard Brogliato.

J. Comput. Nonlinear Dynam 14(9), 091004 (Jul 15, 2019) (10 pages) Paper No: CND-18-1550; doi: 10.1115/1.4044013 History: Received December 11, 2018; Revised May 30, 2019

The paper focuses on the identification of discrete-time bilinear forms in the special case when the external noise (disturbance) is an autoregressive average moving process. The proposed estimation procedure is iterative where, at each iteration, two sets of parameter vectors are estimated interactively. Using the hierarchical technique, a hierarchical generalized extended least squares-based iterative (H-GELSI) algorithm is proposed for avoiding estimating the redundant parameters. In contrast to the hierarchical generalized extended gradient-based iterative (H-GEGI) algorithm, the proposed algorithm can give more accurate parameter estimates. The main results derived in this paper are verified by means of both the computational efficiency comparison and two numerical simulations.

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Figures

Grahic Jump Location
Fig. 1

The Hammerstein nonlinear system

Grahic Jump Location
Fig. 2

The Hammerstein–Wiener nonlinear system

Grahic Jump Location
Fig. 3

The H-GEGI estimation errors δk versus k with different σe2

Grahic Jump Location
Fig. 4

The H-GELSI estimation errors δk versus k with different σe2

Grahic Jump Location
Fig. 5

The O-RLS estimation errors δt versus t with σe12=0.102 and σe22=0.202

Grahic Jump Location
Fig. 6

The H-GELSI estimation errors δk versus k with σe12=0.102 and σe22=0.202

Grahic Jump Location
Fig. 7

The true output and the predicted outputs

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