Decoupling Methods for the Identification of Polynomial Nonlinear Autoregressive Exogenous Input Models
Date
2020-08
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Developing a mathematical model of the system to be controlled is a significant part of a control design process, the more accurate the model, the more precise the control design can be. Since most of the systems around us behave nonlinearly, linear models are not always adequate. Therefore, nonlinear models should be considered. Many different model structures have been used in the literature such as the Volterra series, block-structured models, state-space representations, or nonlinear input-output models. Each of these structures has the ability to represent a large class of nonlinear systems but with its own drawbacks. Many are black-box modeling approaches and do not provide any intuition regarding the system. Many also suffer from the curse of dimensionality, becoming overly complex as the severity of the nonlinearity increases. It would be more practical if a nonlinear system can be approximated by a simpler model that is more accessible and understandable. During this research, the focus was on one of the widely used nonlinear input-output models known as the polynomial Nonlinear Autoregressive eXogenous input (NARX) model, as it represents a large class of nonlinear systems. A decoupling approach is proposed for polynomial NARX models. This technique replaces the multivariate polynomial that characterizes the NARX model with a decoupled model comprising a mixing matrix followed by a bank of univariate polynomials and a summation. While the proposed decoupling algorithm reduces the number of parameters significantly, performing the decoupling involves solving a non-convex optimization, which must be solved iteratively. Different initialization techniques are proposed for this optimization. In addition, identification algorithms are developed in both prediction error and simulation error minimization frameworks. The results of the decoupling approach are verified on two nonlinear identification benchmark problems and show promising outcomes since the number of parameters decreases significantly while the model accuracy remains high. Also, the decoupled model is capable of providing some insight into the identified model, as it is no longer a black-box.
Description
Keywords
System Identification, Control Systems, Optimization
Citation
Karami, K. (2020). Decoupling methods for the identification of Polynomial Nonlinear Autoregressive Exogenous Input Models (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.