Model transformation based distributed stochastic gradient algorithm for multivariate output-error systems

Abstract

This paper is concerned with the parameter estimation problem for the multivariate system disturbed by coloured noises. Since coloured noises will reduce the estimation accuracy, the model transformation technique is employed to whiten the original system without changing the input-output relationship. In order to alleviate the heavy computational burden caused by high-dimensional variables and different types of parameters, the transformed model is divided into several sub-models according to the numbers of outputs. However, after the decomposition, all the sub-models contain a same parameter vector, resulting in many redundant estimates. A model transformation based distributed stochastic gradient (MT-DSG) algorithm is derived to cut down the redundant estimates and exchange the information among the sub-models. Compared with the centralised multivariate generalised stochastic gradient algorithm, the MT-DSG algorithm has more accurate estimates and less computational complexity. Finally, an illustrative example is employed to demonstrate the effectiveness of the proposed method.

Keywords:

• Model transformation
• distributed technique
• stochastic gradient
• parameter estimation
• multivariate system

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data generated or analysed during this study are included in this article.

Additional information

Funding

This work was supported by Research Development Fund of Xi'an Jiaotong-Liverpool University [grant number RDF-21-01-022].

Notes on contributors

Qinyao Liu

Qinyao Liu was born in Chengdu, Sichuan Province, China in 1994. She received her B.Sc. and Ph.D. degrees both from Jiangnan University, Wuxi, China in 2016 and 2021, respectively. Currently, she is a lecturer in the School of Advanced Technology, Xi'an Jiaotong Liverpool University, Suzhou, China. She is the fellow of the Higher Education Academy (FHEA) in UK. Her current research interests include system modeling and identification, and model predictive control.

Feiyan Chen

Feiyan Chen received her M.Sc. degree in the Department of Applied Mathematics from Nanjing University of Finance and Economics (Nanjing, China) in 2013, and Ph. D. degree in the School of Internet of Things Engineering, Jiangnan University (Wuxi, China) in 2017. She is currently an Assistant Professor in the School of Mathematics and Physics, Xi'an Jiaotong Liverpool University. She is the fellow of the Higher Education Academy (FHEA) in UK. Her research interests include processing control and system identification.