Kernelized identification of linear parameter-varying models with linear fractional representation

Manas Mejari, Dario Piga, Roland Toth, Alberto Bemporad

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

The article presents a method for the identification of Linear Parameter-Varying (LPV) models in a Linear Fractional Representation (LFR), which corresponds to a Linear Time-Invariant (LTI) model connected to a scheduling variable dependency via a feedback path. A two-stage identification approach is proposed. In the first stage, Kernelized Canonical Correlation Analysis (KCCA) is formulated to estimate the state sequence of the underlying LPV model. In the second stage, a non-linear least squares cost function is minimized by employing a coordinate descent algorithm to estimate latent variables characterizing the LFR and the unknown model matrices of the LTI block by using the state estimates obtained at the first stage. Here, it is assumed that the structure of the scheduling variable dependent block in the feedback path is fixed. For a special case of affine dependence of the model on the feedback block, it is shown that the optimization problem in the second stage reduces to ordinary least-squares followed by a singular value decomposition.

LanguageEnglish
Title of host publication2019 18th European Control Conference, ECC 2019
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages337-342
Number of pages6
ISBN (Electronic)978-3-907144-00-8
DOIs
StatePublished - 1 Jun 2019
Event18th European Control Conference, ECC 2019 - Naples, Italy
Duration: 25 Jun 201928 Jun 2019

Conference

Conference18th European Control Conference, ECC 2019
CountryItaly
CityNaples
Period25/06/1928/06/19

Fingerprint

Identification (control systems)
Fractional
scheduling
Linear Time
Feedback
Scheduling
Estimate
Coordinate Descent
Canonical Correlation Analysis
estimates
Path
Square Functions
Nonlinear Least Squares
Invariant
Descent Algorithm
Ordinary Least Squares
Matrix Models
Latent Variables
Singular value decomposition
dependent variables

Cite this

Mejari, M., Piga, D., Toth, R., & Bemporad, A. (2019). Kernelized identification of linear parameter-varying models with linear fractional representation. In 2019 18th European Control Conference, ECC 2019 (pp. 337-342). [8796150] Piscataway: Institute of Electrical and Electronics Engineers. DOI: 10.23919/ECC.2019.8796150
Mejari, Manas ; Piga, Dario ; Toth, Roland ; Bemporad, Alberto. / Kernelized identification of linear parameter-varying models with linear fractional representation. 2019 18th European Control Conference, ECC 2019. Piscataway : Institute of Electrical and Electronics Engineers, 2019. pp. 337-342
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Mejari, M, Piga, D, Toth, R & Bemporad, A 2019, Kernelized identification of linear parameter-varying models with linear fractional representation. in 2019 18th European Control Conference, ECC 2019., 8796150, Institute of Electrical and Electronics Engineers, Piscataway, pp. 337-342, 18th European Control Conference, ECC 2019, Naples, Italy, 25/06/19. DOI: 10.23919/ECC.2019.8796150

Kernelized identification of linear parameter-varying models with linear fractional representation. / Mejari, Manas; Piga, Dario; Toth, Roland; Bemporad, Alberto.

2019 18th European Control Conference, ECC 2019. Piscataway : Institute of Electrical and Electronics Engineers, 2019. p. 337-342 8796150.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Mejari M, Piga D, Toth R, Bemporad A. Kernelized identification of linear parameter-varying models with linear fractional representation. In 2019 18th European Control Conference, ECC 2019. Piscataway: Institute of Electrical and Electronics Engineers. 2019. p. 337-342. 8796150. Available from, DOI: 10.23919/ECC.2019.8796150