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Identification of Switching ARX Models for Hybrid Systems Open Access


Other title
error-in-variable models
System Identification
Linear switching systems
Type of item
Degree grantor
University of Alberta
Author or creator
Nazari, Sohail
Supervisor and department
Huang, Biao (Chemical and material engineering department)
Zhao, Qing (Electrical and comupter engineering departmen)
Examining committee member and department
Tavakoli, Mahdi (Electrical and comupter engineering departmen, University of Alberta)
Wang, Qing-Guo (Electrical and comupter engineering departiment, National university of sangapor )
Liu, Jinfeng (Chemical and material engineering department)
Department of Electrical and Computer Engineering
Date accepted
Graduation date
Doctor of Philosophy
Degree level
This dissertation explores the development of a system identification method for Switching ARX (SARX) models for Off-line and Online applications. The switching sequence in SARX models converts the model parameter's estimation into a mix-integer optimization problem. To cope with complexity of the problem, an existing approach that provides an alternative formulation for multi-mode switching models is adopted. The Algebraic Geometric approach addresses the aforementioned problem by executing the identification procedure via two steps. The first step estimates the parameters of the linear ARX model, which is constructed through embedding all the sub-models. The second step retrieves parameters of sub-models from the estimated model obtained in the first step. Although the AG method delivers exact estimation in the deterministic situation, it suffers from a lack of accuracy in the presence of noise. This dissertation investigates the root cause of the mentioned drawback in the AG method and provides a systematic approach to deal with the measurement noise so the identification performance is improved. The proposed Stochastic Algebraic Geometric (SAG) approach reformulates the SARX parameters estimation problem into a "lifted" error-in-variable (EIV) model. Moreover, the characteristics of the proposed EIV model along with the estimation of its parameters are closely investigated. The requirements of a consistent estimation are derived through statistical analysis. In order to calculate the parameters of the sub-models improved retrieving procedures are proposed. In order to extend the application of the SAG into the online parameter estimation, a recursive version of the SAG approach is developed. To achieve this goal, a recursive algorithm for a class of EIV models is derived. Also, a parameter retrieving procedure independent of the data points is developed to determine parameters of the sub-models. To demonstrate a potential application of the proposed approach, a novel fault detection method is developed for linear switching systems. This approach is independent of estimating the sub-model's parameters. By using a residual evaluation method, the incipient changes of the sub-models' parameters can be detected and isolated. The applicability of this approach is demonstrated via simulation examples.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Nazari, S., Zhao, Q., & Huang, B. (2011, June). An improved algebraic geometric solution to the identification of switched ARX models with noise. In American Control Conference (ACC), 2011 (pp. 1230-1235). IEEE.Nazari, S., Zhao, Q., & Huang, B. (2012, June). Matrix-wise approach for identification of multi-mode Switched ARX models with noise. In American Control Conference (ACC), 2012 (pp. 3402-3407). IEEE.Nazari, S., Zhao, Q., & Huang, B (2012), The Recursive Element Wise Weighted Total Least Square Method for Online Parameter Estimation, under revision in system control letters.Nazari, S., Zhao, Q., & Huang, B (2012), An Iterative Algebraic Geometric Approach for Identification of Switched ARX Models with Noise, under revision in IET control theory and application.Nazari, S., Zhao, Q., & Huang, B, Detecting and Isolating Faults in Switching Linear Systems, submitted to IEEE Transactions on Control Systems Technology.

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