Parsimonious model identification via atomic norm minimization

Korkut Bekiroglu, B. Yilmaz, Constantino Manuel Lagoa, M. Sznaier

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

During the past few years a considerably research effort has been devoted to the problem of identifying parsimonious models from experimental data. Since this problem is generically non-convex, these approaches typically rely on relaxations such as Group Lasso or nuclear norm minimization. However, while these approaches usually work well in practice, there is no guarantee that using these surrogates will lead to the simplest model explaining the experimental data. In addition, incorporating stability constraints into the formalism entails a substantial increase in the computational complexity. Alternatively stability and model order constraints can be handled directly using a moments based approach. However, presently this approach is limited to relatively small sized problems, due to its computational complexity. Motivated by these difficulties, recently a new approach has been proposed based on the idea of representing the response of an LTI system as a linear combination of suitably chosen objects (atoms) and the observation that minimizing the atomic norm leads to sparse representations. In this paper we cover the fundamentals of this new approach and show that it leads to a very efficient algorithm, that avoids the need for using regularization steps and automatically incorporates stability constraints. In addition, this approach can be extended to accommodate non-uniform sampling and (unknown) initial conditions. These results are illustrated with several examples, including identification of a very lightly damped structure from time and frequency domain measurements.

Original languageEnglish (US)
Title of host publication2014 European Control Conference, ECC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2392-2397
Number of pages6
ISBN (Electronic)9783952426913
DOIs
StatePublished - Jan 1 2014
Event13th European Control Conference, ECC 2014 - Strasbourg, France
Duration: Jun 24 2014Jun 27 2014

Other

Other13th European Control Conference, ECC 2014
CountryFrance
CityStrasbourg
Period6/24/146/27/14

Fingerprint

Identification (control systems)
Computational complexity
Sampling
Atoms

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Cite this

Bekiroglu, K., Yilmaz, B., Lagoa, C. M., & Sznaier, M. (2014). Parsimonious model identification via atomic norm minimization. In 2014 European Control Conference, ECC 2014 (pp. 2392-2397). [6862636] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ECC.2014.6862636
Bekiroglu, Korkut ; Yilmaz, B. ; Lagoa, Constantino Manuel ; Sznaier, M. / Parsimonious model identification via atomic norm minimization. 2014 European Control Conference, ECC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 2392-2397
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Bekiroglu, K, Yilmaz, B, Lagoa, CM & Sznaier, M 2014, Parsimonious model identification via atomic norm minimization. in 2014 European Control Conference, ECC 2014., 6862636, Institute of Electrical and Electronics Engineers Inc., pp. 2392-2397, 13th European Control Conference, ECC 2014, Strasbourg, France, 6/24/14. https://doi.org/10.1109/ECC.2014.6862636

Parsimonious model identification via atomic norm minimization. / Bekiroglu, Korkut; Yilmaz, B.; Lagoa, Constantino Manuel; Sznaier, M.

2014 European Control Conference, ECC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 2392-2397 6862636.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Bekiroglu K, Yilmaz B, Lagoa CM, Sznaier M. Parsimonious model identification via atomic norm minimization. In 2014 European Control Conference, ECC 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 2392-2397. 6862636 https://doi.org/10.1109/ECC.2014.6862636