12341 of 4
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Consistency and efficiency in continuous-time system identification
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).ORCID iD: 0000-0002-5106-2784
2020 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

Continuous-time system identification deals with the problem of building continuous-time models of dynamical systems from sampled input and output data. In this field, there are two main approaches: indirect and direct. In the indirect approach, a suitable discrete-time model is first determined, and then it is transformed into continuous-time. On the other hand, the direct approach obtains a continuous-time model directly from the sampled data. In both approaches there exists a dichotomy between discrete-time data and continuous-time models, which can induce robustness issues and complications in the theoretical analysis of identification algorithms. These difficulties are addressed in this thesis.

First, we consider the indirect approach to continuous-time system identification. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree one, independent of the relative degree of the strictly proper true system. Inspired by the indirect prediction error method, we propose an indirect-approach estimator that enforces the desired number of poles and zeros in the continuous-time transfer function estimate, and show that the estimator is consistent and asymptotically efficient. A robustification of this method is also developed, by which the estimates are also guaranteed to deliver stable models.

In the second part of the thesis, we analyze asymptotic properties of the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC), which is one of the most popular direct identification methods. This algorithm applies an adaptive prefiltering to the sampled input and output that requires assumptions on the intersample behavior of the signals. We present a comprehensive analysis on the consistency and asymptotic efficiency of the SRIVC estimator while taking into account the intersample behavior of the input signal. Our results show that the SRIVC estimator is generically consistent when the intersample behavior of the input is known exactly and subsequently used in the implementation of the algorithm, and we give conditions under which consistency is not achieved. In terms of statistical efficiency, we compute the asymptotic Cramér-Rao lower bound for an output error model structure with Gaussian noise, and derive the asymptotic covariance of the SRIVC estimates. We conclude that the SRIVC estimator is asymptotically efficient under mild conditions, and that this property can be lost if the intersample behavior of the input is not carefully accounted for in the SRIVC procedure.

Moreover, we propose and analyze the statistical properties of an extension of SRIVC that is able to deal with input signals that cannot be interpolated exactly via hold reconstructions. The proposed estimator is generically consistent for any input reconstructed using zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. Comparisons with the Maximum Likelihood technique and an analysis of the iterations of the method are provided, in order to reveal the influence of the intersample behavior of the output and to propose new robustifications to the SRIVC algorithm.

Place, publisher, year, edition, pages
Stockholm, Sweden: Kungliga Tekniska högskolan, 2020. , p. 135
Series
TRITA-EECS-AVL ; 2020:27
Keywords [en]
System identification; Continuous-time systems; Consistency; Asymptotic efficiency
National Category
Control Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-273176ISBN: 978-91-7873-524-2 (print)OAI: oai:DiVA.org:kth-273176DiVA, id: diva2:1429291
Presentation
2020-06-04, Sal Harry Nyquist, Malvinas väg 10, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20200511

Available from: 2020-05-11 Created: 2020-05-09 Last updated: 2020-05-12Bibliographically approved

Open Access in DiVA

fulltext(2169 kB)50 downloads
File information
File name FULLTEXT01.pdfFile size 2169 kBChecksum SHA-512
a19ebd55bbf6859e813d603e9b6ac74226fc73e0faf66a5d9a9b9b7f212a80be6ebc572293e8646a56539f56597a0eff695de2439fa52c8fec52c24d094a8640
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
González, Rodrigo A.
By organisation
Decision and Control Systems (Automatic Control)
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar
Total: 50 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 166 hits
12341 of 4
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf