Closed-loop time-varying continuous-time recursive subspace-based prediction via principle angles rotation

Miao Yu; Ge Guo; Jianchang Liu; Liangliang Shang

doi:10.1016/j.isatra.2021.04.047

Closed-loop time-varying continuous-time recursive subspace-based prediction via principle angles rotation

ISA Trans. 2022 Mar:122:135-145. doi: 10.1016/j.isatra.2021.04.047. Epub 2021 May 10.

Authors

Miao Yu¹, Ge Guo², Jianchang Liu³, Liangliang Shang⁴

Affiliations

¹ School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, Hebei, China. Electronic address: yumiao@neuq.edu.cn.
² School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, Hebei, China; State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning, China.
³ State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning, China; College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, China.
⁴ School of Electrical Engineering, Nantong University, Nantong, Jiangsu, China.

PMID: 33992417
DOI: 10.1016/j.isatra.2021.04.047

Abstract

This paper presents a closed-loop time-varying continuous-time recursive subspace-based prediction method utilizing principle angles rotation. A simple linear mapping can be provided by generalized Poisson moment functionals, which can deal with the time-derivatives problems of input-output Hankel matrices. The parity space employed in fault detection field is adopted instead of using the observable subspace. The system matrices are estimated consistently by the instrumental variable method and principal component analysis, which solves the identification problems of biased results for the system operating in closed-loop with a feedback controller. The system matrices are predicted by the principle angles rotation of the signal subspaces spanned from the extended observability matrices. The effectiveness of the proposed method is illustrated by the numerical simulations and real applications.

Keywords: Closed-loop identification; Generalized Poisson moment functionals; Principal component analysis; Principle angles rotation; Subspace identification; Subspace prediction.