A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems. (March 2017)

• Record Type: Journal Article
• Authors: Mu, Biqiang; Bai, Er-Wei; Zheng, Wei Xing; Zhu, Quanmin
• Is Part Of: Automatica. Volume 77(2017)
• Page Start: 322
• Page End: 335
• Publication Date: 2017-03
• Subjects: Nonlinear rational systems -- Nonlinear least squares estimators -- Two-step estimators -- N-consistent estimators -- Gauss–Newton algorithms; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.11.009
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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.