NDLI: Worst-case system identification in $H_{∞}:$ validation of apriori information, essentially optimal algorithms, and error bounds

Content Provider	IEEE Xplore Digital Library
Author	Chen, Jie Nett, Carl N. Fan, Michael K.H.
Copyright Year	1992
Description	Author affiliation: Assistant Professor, School of Electrical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, (404) 853-9828, eefacmf@prism.gatech.edu (Fan, Michael K.H.) \|\| Associate Professor and Director, Laboratory for Identification and Control of Complex Highly Uncertain Systems (LICCHUS), School of Aerospace Engineering, Georgia Institute of Techology, Atlanta, GA 30332-0150, (404) 894-8200, cn4@prism.gatech.edu (Nett, Carl N.) \|\| Postdoctoral Fellow, Schools of Aerospace and Electrical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, (404) 853-0173, chen@licchus1.gatech.edu (Chen, Jie)
Abstract	This paper is concerned with a particular control-oriented system identification problem recently considered by several authors. This problem has been referred to as the problem of worst-case system identification in $H_{∞}$ in the literature. The formulation of this problem is worst-case/deterministic in nature. The available apriori information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The available aposteriori information consists-of a finite number of noisy plant point frequency response samples. The objective is to identify the plant transfer function in $H_{∞}$ using the available apriori and aposteriori information. In this paper we resolve several important open issues pertaining to this problem. First, a method is presented for developing confidence that the available apriori information is correct. This method requires the solution of a certain nondifferentiable convex programming problem. Second, an essentially optimal identification algorithm is given for this problem. This algorithm is (worst-case strongy) optimal to within a factor of two. Finally, new upper and lower bounds on the optimal identification error for this problem are derived and used to estimate the identification error associated with the algorithm presented here. Interestingly, the development of each of the results described above draws heavily upon the classical Nevanlinna-Pick optimal interpolation theory. As such, the results of this paper establish a clear link between the areas of system identification and optimal interpolation theory.
Starting Page	251
Ending Page	257
File Size	872370
Page Count	7
File Format	PDF
ISBN	0780302109
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1992-06-24
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	System identification Interpolation Upper bound Noise level Control systems Stability Frequency response Aerospace engineering Space technology Transfer functions
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in