On embeddings and inverse embeddings of input design for regularized system identification

Mu，Biqiang1; Chen，Tianshi2; Kong，He3,4; Jiang，Bo5; Wang，Lei6; Wu，Junfeng2,6

2023

10.1016/j.automatica.2022.110673

AUTOMATICA   Impact Factor & Quartile

0005-1098

1873-2836

Input design is an important problem for system identification and has been well studied for the classical system identification, i.e., the maximum likelihood/prediction error method. For the emerging regularized system identification, the study on input design has just started, and it is often formulated as a non-convex optimization problem minimizing a scalar measure of the Bayesian mean squared error matrix subject to certain constraints. Among the state-of-art input design techniques for regularized system identification is the so-called quadratic mapping and inverse embedding (QMIE) method. Based on the quadratic mapping between the input and its covariance, the QMIE method is first to obtain the optimal autocovariance by solving a transformed convex optimization problem and then to find all the inputs corresponding to the optimal autocovariance by the time domain inverse embedding (TDIE). In this paper, we report some new results on the embeddings/inverse embeddings of the QMIE method. Firstly, we present a general result on the frequency domain inverse embedding (FDIE) that is to find the inverse of the quadratic mapping described by the discrete-time Fourier transform. Then we show the relation between the TDIE and the FDIE from a graph signal processing perspective. Finally, motivated by this perspective, we further propose a graph induced embedding and its inverse, which include the previously introduced embeddings as special cases. This deepens our understanding of input design from a broader perspective beyond the time domain and frequency domain viewpoints.

Discrete-time Fourier transform Graph signal processing Input design Inverse embedding Regularized system identification

SCI

English

Others

National Natural Science Foundation of China[11971239];National Key Research and Development Program of China[2018YFA0703800];Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions[21KJA110002];National Natural Science Foundation of China[61773329];National Natural Science Foundation of China[62273287];

Automation & Control Systems ; Engineering

Automation & Control Systems ; Engineering, Electrical & Electronic

WOS:000953942300023

PERGAMON-ELSEVIER SCIENCE LTD

ENGINEERING

2-s2.0-85141224500

Scopus

1.Key Laboratory of Systems and Control,Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,100190,China
2.School of Data Science and Shenzhen Research Institute of Big Data,The Chinese University of Hong Kong,Shenzhen,518172,China
3.Shenzhen Key Laboratory of Biomimetic Robotics and Intelligent Systems,Department of Mechanical and Energy Engineering,Southern University of Science and Technology,Shenzhen,518055,China
4.Guangdong Provincial Key Laboratory of Human-Augmentation and Rehabilitation Robotics in Universities,Southern University of Science and Technology,Shenzhen,518055,China
5.Key Laboratory for NSLSCS of Jiangsu Province,School of Mathematical Sciences,Nanjing Normal University,Nanjing,China
6.College of Control Science and Engineering,Zhejiang University,Hangzhou,China

Mu，Biqiang,Chen，Tianshi,Kong，He,et al. On embeddings and inverse embeddings of input design for regularized system identification[J]. AUTOMATICA,2023,147.

Mu，Biqiang,Chen，Tianshi,Kong，He,Jiang，Bo,Wang，Lei,&Wu，Junfeng.(2023).On embeddings and inverse embeddings of input design for regularized system identification.AUTOMATICA,147.

Mu，Biqiang,et al."On embeddings and inverse embeddings of input design for regularized system identification".AUTOMATICA 147(2023).