Weighted hierarchical stochastic gradient identification algorithms for ARX models

Abstract

In this paper, a weighted hierarchical stochastic gradient algorithm and a latest estimation-based weighted hierarchical stochastic gradient algorithm for ARX models are proposed. Different from some existing stochastic gradient algorithms, the correction term of the developed algorithms is in a weighted form of the correction terms in the current and last recursive steps of the hierarchical stochastic gradient algorithm. Further, the convergence property of the presented latest estimation-based weighted hierarchical stochastic gradient algorithm is analysed. It is illustrated by a numerical example that both the weighted hierarchical stochastic gradient and the latest estimation-based weighted hierarchical stochastic gradient algorithms possess higher convergence accuracy compared with some existing hierarchical stochastic gradient algorithms if the weighting factor is appropriately chosen.

Keywords:

• System identification
• parameter identification
• convergence analysis

Disclosure statement

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

Additional information

Funding

This work was supported by National Natural Science Foundation of China for Excellent Young Scholars [grant number 61822305], by Shenzhen Municipal Project for International Cooperation with Project No. GJHZ20180420180849805, by The Fundamental Research Funds for the Central Universities [grant number HIT.BRETIV.201907], by Shenzhen Municipal Basic Research Project for Discipline Layout with Project No. JCYJ20170811160715620, by Guangdong Natural Science Foundation [grant numbers 2020A1515011091 and 2019A1515011576].

Notes on contributors

Rui-Qi Dong

Rui-Qi Dong was born in Shandong, China, in 1992. She received the B.Eng. degree in automation from the Shandong University of Technology, in 2014, and the M.Eng. degree in control science and engineering from Harbin Institute of Technology Shenzhen Graduate School in 2016. She was a recipient of the National Scholarship in 2016, and the First Prize Scholarship of HIT from 2014 to 2016.

She is currently pursuing the Ph.D. degree in Harbin Institute of Technology, Shenzhen. Her research interests include system identification and attitude control of spacecraft.

Ying Zhang

Ying Zhang was born in Jilin, China. She received the M.Eng. degree in control theory and control engineering from Harbin University of Science and Technology in 2003, and the Ph.D. degree in control science and engineering from Harbin Institute of Technology in 2007. From 2007 to 2010, she was a Postdoctoral Researcher with Harbin Institute of Technology Shenzhen Graduate School, where she became an Assistant Professor in 2010, and an Associate Professor in 2011. She is currently an Associate Professor with Harbin Institute of Technology, Shenzhen. Her main research interests include spacecraft control, robust control and filter theory, and networked control.

Ai-Guo Wu

Ai-Guo Wu was born in Gong’an, Hubei, China, in 1980. He received the B.Eng. degree in automation, the M.Eng. degree in navigation, guidance and control, and the Ph.D. degree in control science and engineering from Harbin Institute of Technology, in 2002, 2004, and 2008, respectively. In 2008, he joined the Harbin Institute of Technology Shenzhen Graduate School as an Assistant Professor, where he was promoted to a Professor in 2012. He was a Research Fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, from 2009 to 2011. He was a Visiting Professor with the Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, Australia, from 2013 to 2014. Since 2018, he has been a Professor with Harbin Institute of Technology, Shenzhen.

His research interests include spacecraft control, descriptor systems, conjugate product of polynomials, switched systems, and robust control. He has authored/co-authored one English monograph and over 70 SCI journal papers. He received the National Natural Science Award (Second Prize) from China in 2015, and the National Excellent Doctoral Dissertation Award from the Academic Degrees Committee of the State Council and the Ministry of Education of China in 2011. He was supported by the Program for New Century Excellent Talents in University in 2011, and by the National Natural Science Foundation of China for Excellent Young Scholars in 2018.

Dr. Wu has been a Reviewer for American Mathematical Review, since 2007. He was an Outstanding Reviewer for IEEE TRANSACTIONS ON AUTOMATIC CONTROL in 2010. He has been serving as a Regional Editor for Nonlinear Dynamics and Systems Theory since 2015, and an International Subject Editor for Applied Mathematical Modelling since 2017.