### 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.

Language | English |
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Title of host publication | 2019 18th European Control Conference, ECC 2019 |

Place of Publication | Piscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 337-342 |

Number of pages | 6 |

ISBN (Electronic) | 978-3-907144-00-8 |

DOIs | |

State | Published - 1 Jun 2019 |

Event | 18th European Control Conference, ECC 2019 - Naples, Italy Duration: 25 Jun 2019 → 28 Jun 2019 |

### Conference

Conference | 18th European Control Conference, ECC 2019 |
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Country | Italy |

City | Naples |

Period | 25/06/19 → 28/06/19 |

### Fingerprint

### Cite this

*2019 18th European Control Conference, ECC 2019*(pp. 337-342). [8796150] Piscataway: Institute of Electrical and Electronics Engineers. DOI: 10.23919/ECC.2019.8796150

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Kernelized identification of linear parameter-varying models with linear fractional representation

AU - Mejari,Manas

AU - Piga,Dario

AU - Toth,Roland

AU - Bemporad,Alberto

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85071590415&partnerID=8YFLogxK

U2 - 10.23919/ECC.2019.8796150

DO - 10.23919/ECC.2019.8796150

M3 - Conference contribution

SP - 337

EP - 342

BT - 2019 18th European Control Conference, ECC 2019

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -