A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems

Mu, Biqiang; Bai, Er Wei; Zheng, Wei Xing; Zhu, Quanmin

Abstract

© 2016 Elsevier Ltd This paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs. Despite its long history, a globally consistent identification algorithm remains illusive. This paper proposes a globally convergent identification algorithm for such nonlinear rational systems. To the best of our knowledge, this is the first globally convergent algorithm for the nonlinear rational systems. The technique employed is a two-step estimator. Though two-step estimators are known to produce consistent nonlinear least squares estimates if a N consistent estimate can be determined in the first step, how to find such a N consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two-step estimators. The technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step. This is achieved by involving model transformation, bias analysis, noise variance estimation, and bias compensation in the paper. Two simulation examples and a practical example are provided to verify the good performance of the proposed two-step estimator.

Citation

Mu, B., Bai, E. W., Zheng, W. X., & Zhu, Q. (2017). A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems. Automatica, 77, 322-335. https://doi.org/10.1016/j.automatica.2016.11.009

• Journal Article Type: Article
• Acceptance Date: Oct 4, 2016
• Online Publication Date: Jan 17, 2017
• Publication Date: Mar 1, 2017
• Deposit Date: Jan 18, 2017
• Publicly Available Date: Jan 17, 2018
• Journal: Automatica
• Print ISSN: 0005-1098
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 77
• Pages: 322-335
• DOI: https://doi.org/10.1016/j.automatica.2016.11.009
• Keywords: nonlinear rational systems, nonlinear least squares estimators, two-step estimators, view the MathML source-consistent estimators, gauss–newton algorithms
• Public URL: https://uwe-repository.worktribe.com/output/897809
• Publisher URL: http://dx.doi.org/10.1016/j.automatica.2016.11.009