Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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
A convex optimization approach to complexity constrained analytic interpolation with applications to ARMA estimation and robust control
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2005 (English)Doctoral thesis, monograph (Other scientific)
Abstract [en]

Analytical interpolation theory has several applications in systems and control. In particular, solutions of low degree, or more generally of low complexity, are of special interest since they allow for synthesis of simpler systems. The study of degree constrained analytic interpolation was initialized in the early 80's and during the past decade it has had significant progress.

This thesis contributes in three different aspects to complexity constrained analytic interpolation: theory, numerical algorithms, and design paradigms. The contributions are closely related; shortcomings of previous design paradigms motivate development of the theory, which in turn calls for new robust and efficient numerical algorithms.

Mainly two theoretical developments are studied in the thesis. Firstly, the spectral Kullback-Leibler approximation formulation is merged with simultaneous cepstral and covariance interpolation. For this formulation, both uniqueness of the solution, as well as smoothness with respect to data, is proven. Secondly, the theory is generalized to matrix-valued interpolation, but then only allowing for covariance-type interpolation conditions. Again, uniqueness and smoothness with respect to data is proven.

Three algorithms are presented. Firstly, a refinement of a previous algorithm allowing for multiple as well as matrix-valued interpolation in an optimization framework is presented. Secondly, an algorithm capable of solving the boundary case, that is, with spectral zeros on the unit circle, is given. This also yields an inherent numerical robustness. Thirdly, a new algorithm treating the problem with both cepstral and covariance conditions is presented.

Two design paradigms have sprung out of the complexity constrained analytical interpolation theory. Firstly, in robust control it enables low degree Hinf controller design. This is illustrated by a low degree controller design for a benchmark problem in MIMO sensitivity shaping. Also, a user support for the tuning of controllers within the design paradigm for the SISO case is presented. Secondly, in ARMA estimation it provides unique model estimates, which depend smoothly on the data as well as enables frequency weighting. For AR estimation, a covariance extension approach to frequency weighting is discussed, and an example is given as an illustration. For ARMA estimation, simultaneous cepstral and covariance matching is generalized to include prefiltering. An example indicates that this might yield asymptotically efficient estimates.

Place, publisher, year, edition, pages
Stockholm: KTH , 2005. , ix, 125 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 05:01
Keyword [en]
Mathematical optimization, systems theory, analytic interpolation, moment matching, Nevanlinna-Pick interpolation, spectral estimation, convex optimization
Keyword [sv]
Optimeringslära, systemteori
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-117ISBN: 91-7283-950-3 (print)OAI: oai:DiVA.org:kth-117DiVA: diva2:6958
Public defence
2005-02-07, Kollegiesalen, Valhallavägen 79, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20100928Available from: 2005-02-04 Created: 2005-02-04 Last updated: 2010-09-28Bibliographically approved

Open Access in DiVA

fulltext(995 kB)1995 downloads
File information
File name FULLTEXT01.pdfFile size 995 kBChecksum MD5
55c13867b379dffd54688ad47e76b60f86db5e35fdf9d30061a104bddb78df6b1e16d236
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Blomqvist, Anders
By organisation
Optimization and Systems Theory
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 1995 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: 942 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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