<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.</p></abstract>

A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

Institute of Control and Computation Engineering

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a...

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

Published Online: Sep 28, 2019

Page range: 571 - 580

Received: Dec 13, 2018

Accepted: Apr 10, 2019

DOI: https://doi.org/10.2478/amcs-2019-0042

Keywords
nonlinear systems, parameter estimation, dynamic models, polynomial models

© 2019 Andrzej Janczak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

Published Online: Sep 28, 2019

Page range: 571 - 580

Received: Dec 13, 2018

Accepted: Apr 10, 2019

DOI: https://doi.org/10.2478/amcs-2019-0042

Keywordsnonlinear systems, parameter estimation, dynamic models, polynomial models

© 2019 Andrzej Janczak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
nonlinear systems, parameter estimation, dynamic models, polynomial models