Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter

Adrian-Josue Guel-Cortez; Eun-Jin Kim; Harold-R. Chamorro

doi:10.1109/icfda58234.2023.10153299

Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter

Adrian-Josue Guel-Cortez, Eun-Jin Kim, Harold-R. Chamorro

Research Centre for Fluid and Complex Systems

KTH Royal Institute of Technology

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

Abstract

As fractional-order models increasingly appear as an option to describe complex systems, they generate a demand for parameter estimation methods in the time and frequency domain. The extended Kalman filter (EKF) is a promising technique in the time domain, but it is sensitive to the initial conditions of the state and error covariance matrices. In the case of integer-order systems, evolutionary algorithms (EAs) can tackle EKF’s sensitiveness issues. The algorithm usually uses EAs to optimise the initial conditions for the EK, leading to a better estimate of the system parameters and states. Here, we extend this methodology to fractional-order models to estimate the model’s fractional order and parameters. Finally, we demonstrate the effectiveness of this methodology on a simple mechanical model.

Original language	English
Title of host publication	2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)
Publisher	IEEE
Number of pages	6
ISBN (Electronic)	979-8-3503-2168-5
ISBN (Print)	979-8-3503-2169-2
DOIs	https://doi.org/10.1109/icfda58234.2023.10153299
Publication status	Published - 20 Jun 2023
Event	2023 International Conference on Fractional Differentiation and Its Applications - Ajman University, Ajman, United Arab Emirates Duration: 14 Mar 2023 → 16 Mar 2023 https://www.aconf.org/conf_186827.html

Publication series

Name	2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)
Publisher	IEEE

Conference

Conference	2023 International Conference on Fractional Differentiation and Its Applications
Abbreviated title	ICFDA
Country/Territory	United Arab Emirates
City	Ajman
Period	14/03/23 → 16/03/23
Internet address	https://www.aconf.org/conf_186827.html

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Keywords

Fractional-order Systems
Parameter Identification
Extended Kalman Filter
Genetic Algorithms
Fractional Calculus

Access to Document

10.1109/icfda58234.2023.10153299

Cite this

Guel-Cortez, A.-J., Kim, E.-J., & Chamorro, H.-R. (2023). Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter. In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA) (2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)). IEEE. https://doi.org/10.1109/icfda58234.2023.10153299

Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter. / Guel-Cortez, Adrian-Josue; Kim, Eun-Jin; Chamorro, Harold-R.
2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE, 2023. (2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)).

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

Guel-Cortez, A-J, Kim, E-J & Chamorro, H-R 2023, Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter. in 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), IEEE, 2023 International Conference on Fractional Differentiation and Its Applications, Ajman, United Arab Emirates, 14/03/23. https://doi.org/10.1109/icfda58234.2023.10153299

Guel-Cortez AJ, Kim EJ, Chamorro HR. Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter. In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE. 2023. (2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)). doi: 10.1109/icfda58234.2023.10153299

Guel-Cortez, Adrian-Josue ; Kim, Eun-Jin ; Chamorro, Harold-R. / Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter. 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE, 2023. (2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)).

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N2 - As fractional-order models increasingly appear as an option to describe complex systems, they generate a demand for parameter estimation methods in the time and frequency domain. The extended Kalman filter (EKF) is a promising technique in the time domain, but it is sensitive to the initial conditions of the state and error covariance matrices. In the case of integer-order systems, evolutionary algorithms (EAs) can tackle EKF’s sensitiveness issues. The algorithm usually uses EAs to optimise the initial conditions for the EK, leading to a better estimate of the system parameters and states. Here, we extend this methodology to fractional-order models to estimate the model’s fractional order and parameters. Finally, we demonstrate the effectiveness of this methodology on a simple mechanical model.

AB - As fractional-order models increasingly appear as an option to describe complex systems, they generate a demand for parameter estimation methods in the time and frequency domain. The extended Kalman filter (EKF) is a promising technique in the time domain, but it is sensitive to the initial conditions of the state and error covariance matrices. In the case of integer-order systems, evolutionary algorithms (EAs) can tackle EKF’s sensitiveness issues. The algorithm usually uses EAs to optimise the initial conditions for the EK, leading to a better estimate of the system parameters and states. Here, we extend this methodology to fractional-order models to estimate the model’s fractional order and parameters. Finally, we demonstrate the effectiveness of this methodology on a simple mechanical model.

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Parameter Estimation of Fractional-Order Systems via Evolutionary Algorithms and the Extended Fractional Kalman Filter

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