Finite Time LTI System Identification
Name
19-725.pdf
Description
Published version
Size
783.52 KB
Format
Adobe PDF
Checksum (MD5)
636953d8d7404ac4443f1c3728e6b621
Author(s)
Sarkar, Tuhin
Rakhlin, Alexander
Dahleh, Munther A
Date Issued
2021
Journal
JOURNAL OF MACHINE LEARNING RESEARCH
Citation
Sarkar, Tuhin, Rakhlin, Alexander and Dahleh, Munther A. 2021. "Finite Time LTI System Identification." JOURNAL OF MACHINE LEARNING RESEARCH, 22.
Version
Final published version
Abstract
We address the problem of learning the parameters of a stable linear time invariant (LTI)
system with unknown latent space dimension, or order, from a single time–series of noisy
input-output data. We focus on learning the best lower order approximation allowed by finite
data. Motivated by subspace algorithms in systems theory, where the doubly infinite system
Hankel matrix captures both order and good lower order approximations, we construct a
Hankel-like matrix from noisy finite data using ordinary least squares. This circumvents the
non-convexities that arise in system identification, and allows accurate estimation of the
underlying LTI system. Our results rely on careful analysis of self-normalized martingale
difference terms that helps bound identification error up to logarithmic factors of the lower
bound. We provide a data-dependent scheme for order selection and find an accurate
realization of system parameters, corresponding to that order, by an approach that is closely
related to the Ho-Kalman subspace algorithm. We demonstrate that the proposed model
order selection procedure is not overly conservative, i.e., for the given data length it is
not possible to estimate higher order models or find higher order approximations with
reasonable accuracy.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://www.jmlr.org/papers/volume22/19-725/19-725.pdf
