On the uncertainty modelling for linear continuous-time systems utilising sampled data and Gaussian mixture models

Rafael Orellana; María Coronel; Rodrigo Carvajal; Ramon A. Delgado; Pedro Escárate; Juan C. Agüero

doi:10.1016/j.ifacol.2021.08.424

On the uncertainty modelling for linear continuous-time systems utilising sampled data and Gaussian mixture models

Rafael Orellana, María Coronel, Rodrigo Carvajal, Ramon A. Delgado, Pedro Escárate, Juan C. Agüero

Research output: Contribution to journal › Conference article › peer-review

Abstract

In this paper a Maximum Likelihood estimation algorithm for model error modelling in a continuous-time system is developed utilising sampled data and a Stochastic Embedding approach. Orthonormal basis functions are used to model both the continuous-time nominal model and the error-model. The stochastic properties of the error-model distribution are defined by using a Gaussian mixture model. For the estimation of the nominal model and the error-model distribution we develop a technique based on the Expectation-Maximization algorithm using sampled data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

Original language	English
Pages (from-to)	589-594
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	54
Issue number	7
DOIs	https://doi.org/10.1016/j.ifacol.2021.08.424
State	Published - 1 Jul 2021
Externally published	Yes
Event	19th IFAC Symposium on System Identification, SYSID 2021 - Padova, Italy Duration: 13 Jul 2021 → 16 Jul 2021

Keywords

Continuous-time model
Discrete-time model
Gaussian mixture model
Maximum Likelihood
Stochastic embedding

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10.1016/j.ifacol.2021.08.424

Cite this

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title = "On the uncertainty modelling for linear continuous-time systems utilising sampled data and Gaussian mixture models",

abstract = "In this paper a Maximum Likelihood estimation algorithm for model error modelling in a continuous-time system is developed utilising sampled data and a Stochastic Embedding approach. Orthonormal basis functions are used to model both the continuous-time nominal model and the error-model. The stochastic properties of the error-model distribution are defined by using a Gaussian mixture model. For the estimation of the nominal model and the error-model distribution we develop a technique based on the Expectation-Maximization algorithm using sampled data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.",

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AU - Orellana, Rafael

AU - Coronel, María

AU - Carvajal, Rodrigo

AU - Delgado, Ramon A.

AU - Escárate, Pedro

AU - Agüero, Juan C.

PY - 2021/7/1

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N2 - In this paper a Maximum Likelihood estimation algorithm for model error modelling in a continuous-time system is developed utilising sampled data and a Stochastic Embedding approach. Orthonormal basis functions are used to model both the continuous-time nominal model and the error-model. The stochastic properties of the error-model distribution are defined by using a Gaussian mixture model. For the estimation of the nominal model and the error-model distribution we develop a technique based on the Expectation-Maximization algorithm using sampled data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

AB - In this paper a Maximum Likelihood estimation algorithm for model error modelling in a continuous-time system is developed utilising sampled data and a Stochastic Embedding approach. Orthonormal basis functions are used to model both the continuous-time nominal model and the error-model. The stochastic properties of the error-model distribution are defined by using a Gaussian mixture model. For the estimation of the nominal model and the error-model distribution we develop a technique based on the Expectation-Maximization algorithm using sampled data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

KW - Continuous-time model

KW - Discrete-time model

KW - Gaussian mixture model

KW - Maximum Likelihood

KW - Stochastic embedding

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T2 - 19th IFAC Symposium on System Identification, SYSID 2021

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On the uncertainty modelling for linear continuous-time systems utilising sampled data and Gaussian mixture models

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Keywords

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