Approximability models and optimal system identification

This article considers the problem of optimally recovering stable linear time-invariant systems observed via linear measurements made on their transfer functions. A common modeling assumption is replaced here by the related assumption that the transfer functions belong to a model set described by ap...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics of control, signals, and systems signals, and systems, 2020-03, Vol.32 (1), p.19-41
Main Authors: Ettehad, Mahmood, Foucart, Simon
Format: Article
Language:English
Subjects:
Algorithms
Communications Engineering
Control
Hilbert space
Mathematical analysis
Mathematics
Mathematics and Statistics
Mechatronics
Networks
Optimization
Original Article
Recovery
Robotics
System identification
Systems Theory
Time invariant systems
Toruses
Transfer functions
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article considers the problem of optimally recovering stable linear time-invariant systems observed via linear measurements made on their transfer functions. A common modeling assumption is replaced here by the related assumption that the transfer functions belong to a model set described by approximation capabilities. Capitalizing on recent optimal recovery results relative to such approximability models, we construct some optimal algorithms and characterize the optimal performance for the identification and evaluation of transfer functions in the framework of the Hardy Hilbert space and of the disk algebra. In particular, we determine explicitly the optimal recovery performance for frequency measurements taken at equispaced points on an inner circle or on the torus.
ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-020-00253-z