Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses

ABSTRACT

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two sub-algorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance.

KEYWORDS:

• Parameter estimation
• hierarchical principle
• iterative estimation
• Newton search
• least squares

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ling Xu http://orcid.org/0000-0002-5040-5634

Feng Ding http://orcid.org/0000-0002-2721-2025

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 6187311], the 111 Project [grant number B12018], the National First-Class Discipline Program of Light Industry Technology and Engineering [grant number LITE2018-26], the Qing Lan Project and the Postdoctoral Science Foundation of Jiangsu Province [grant number 1701020A].

Notes on contributors

Ling Xu

Ling Xu was born in Tianjin, China. She received the Master and Ph.D. degrees from the Jiangnan University (Wuxi, China) in 2005 and 2015. She has been an Associate Professor since 2015. She is a Colleges and Universities ‘Blue Project’ Young Teacher (Jiangsu, China). Her research interests include process control, parameter estimation and signal modelling.

Feng Ding

Feng Ding received his B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and his M.Sc. and Ph.D. degrees both from the Tsinghua University in 1991 and 1994, respectively. He has been a professor in the School of Internet of Things Engineering at the Jiangnan University (Wuxi, China) since 2004. His current research interests include model identification and adaptive control. He authored four books on System Identification.

Quanmin Zhu

Quanmin Zhu is professor in control systems at the Department of Engineering Design and Mathematics,University of the West of England, Bristol, UK. He obtained his MSc in Harbin Institute of Technology, China in 1983 and PhD in Faculty of Engineering, University of Warwick, UK in 1989. Hismain research interest is in the area of nonlinear system modelling, identification, and control. He has published over 200 papers on these topics, edited five Springer books and one book for the other publisher, and provided consultancy to various industries. Currently Professor Zhu is acting as editor of International Journal of Modelling, Identification and Control, editor of International Journal of Computer Applications in Technology.