Global and asymptotically efficient identification of nonlinear rational systems via a two-step method

Biqiang Mu; Er-Wei Bai; Wei Xing Zheng

doi:10.1109/ChiCC.2016.7553658

Back

Conference proceeding

Global and asymptotically efficient identification of nonlinear rational systems via a two-step method

Biqiang Mu, Er-Wei Bai and Wei Xing Zheng

2016 35th Chinese Control Conference (CCC), Vol.2016-, pp.1987-1994

07/2016

DOI: 10.1109/ChiCC.2016.7553658

View Online

Abstract

Identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs is considered in this paper. Although this problem has a long history, there is still lack of a globally consistent identification algorithm for such identification problem. This paper develops a globally consistent algorithm by the following steps: model transformation, bias analysis, noise variance estimation, and compensation. First, the paper studies the prediction error type estimator (nonlinear least square estimators) and the corresponding solving algorithm (Gauss-Newton algorithms). It is shown that the Gauss-Newton algorithm is locally convergent but actually asymptotically efficient by calculating the Cramér-Rao lower bound under Gaussian observation noises. This motivates that a global and asymptotically efficient estimator can be constructed by combining the proposed globally consistent estimator with the Gauss-Newton algorithm. So, a two-step method is proposed, which consists of first executing the globally consistent algorithm and then applying the Gauss-Newton algorithm with the consistent estimate serving as the initial value. A simulation example is provided to verify the good performance of the proposed two-step method.

Algorithm design and analysis

asymptotical efficiency

Autoregressive processes

Convergence

corrected least squares

Gauss-Newton algorithms

global convergence

Linear programming

local convergence

nonlinear least squares

Nonlinear rational systems

Nonlinear systems

Prediction algorithms

Details

Title: Subtitle: Global and asymptotically efficient identification of nonlinear rational systems via a two-step method
Creators: Biqiang Mu - Chinese Academy of Sciences
Er-Wei Bai - University of Iowa
Wei Xing Zheng - University of Sydney
Resource Type: Conference proceeding
Publication Details: 2016 35th Chinese Control Conference (CCC), Vol.2016-, pp.1987-1994
Publisher: TCCT
DOI: 10.1109/ChiCC.2016.7553658
ISSN: 1934-1768
eISSN: 2161-2927
Language: English
Date published: 07/2016
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984197233402771

Metrics

19 Record Views