Non-asymptotic State Estimation of Linear Reaction Diffusion Equation using Modulating Functions

Lilia Ghaffour; Matti Noack; Johann Reger; Taous-Meriem Laleg-Kirati

Non-asymptotic State Estimation of Linear Reaction Diffusion Equation using Modulating Functions

Lilia Ghaffour, Matti Noack, Johann Reger, Taous-Meriem Laleg-Kirati

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, we propose a non-asymptotic state estimation method for the linear reaction diffusion equation with general boundary conditions. The method is based on the modulating function approach utilizing a modulation functional in time and space. This results in a signal model control problem for a system of auxiliary PDEs in order to determine the modulation kernels. First, the algorithm is mathematically derived and then numerical simulations are presented for illustrating the good performance of the proposed approach and demonstrating the efficient implementation scheme.

Original language	English (US)
Title of host publication	IFAC World Congress 2020
Publisher	Elsevier
State	Published - 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): BAS/1/1627-01-01
Acknowledgements: This work has been supported by the King Abdullah University of Science and Technology (KAUST) Base Research Fund (BAS/1/1627-01-01) to Taous Meriem Laleg.This project also has received funding from the European Union’s Horizon 2020 research and innovation program under Marie Sk lodowska-Curie grant agreement No. 824046.

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@inproceedings{6266839e5d964c578c306fdb3e4399a0,

title = "Non-asymptotic State Estimation of Linear Reaction Diffusion Equation using Modulating Functions",

abstract = "In this paper, we propose a non-asymptotic state estimation method for the linear reaction diffusion equation with general boundary conditions. The method is based on the modulating function approach utilizing a modulation functional in time and space. This results in a signal model control problem for a system of auxiliary PDEs in order to determine the modulation kernels. First, the algorithm is mathematically derived and then numerical simulations are presented for illustrating the good performance of the proposed approach and demonstrating the efficient implementation scheme.",

author = "Lilia Ghaffour and Matti Noack and Johann Reger and Taous-Meriem Laleg-Kirati",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): BAS/1/1627-01-01 Acknowledgements: This work has been supported by the King Abdullah University of Science and Technology (KAUST) Base Research Fund (BAS/1/1627-01-01) to Taous Meriem Laleg.This project also has received funding from the European Union{\textquoteright}s Horizon 2020 research and innovation program under Marie Sk lodowska-Curie grant agreement No. 824046.",

year = "2020",

language = "English (US)",

booktitle = "IFAC World Congress 2020",

publisher = "Elsevier",

address = "Netherlands",

}

TY - GEN

T1 - Non-asymptotic State Estimation of Linear Reaction Diffusion Equation using Modulating Functions

AU - Ghaffour, Lilia

AU - Noack, Matti

AU - Reger, Johann

AU - Laleg-Kirati, Taous-Meriem

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): BAS/1/1627-01-01 Acknowledgements: This work has been supported by the King Abdullah University of Science and Technology (KAUST) Base Research Fund (BAS/1/1627-01-01) to Taous Meriem Laleg.This project also has received funding from the European Union’s Horizon 2020 research and innovation program under Marie Sk lodowska-Curie grant agreement No. 824046.

PY - 2020

Y1 - 2020

N2 - In this paper, we propose a non-asymptotic state estimation method for the linear reaction diffusion equation with general boundary conditions. The method is based on the modulating function approach utilizing a modulation functional in time and space. This results in a signal model control problem for a system of auxiliary PDEs in order to determine the modulation kernels. First, the algorithm is mathematically derived and then numerical simulations are presented for illustrating the good performance of the proposed approach and demonstrating the efficient implementation scheme.

AB - In this paper, we propose a non-asymptotic state estimation method for the linear reaction diffusion equation with general boundary conditions. The method is based on the modulating function approach utilizing a modulation functional in time and space. This results in a signal model control problem for a system of auxiliary PDEs in order to determine the modulation kernels. First, the algorithm is mathematically derived and then numerical simulations are presented for illustrating the good performance of the proposed approach and demonstrating the efficient implementation scheme.

UR - http://hdl.handle.net/10754/664914

M3 - Conference contribution

BT - IFAC World Congress 2020

PB - Elsevier

ER -

Non-asymptotic State Estimation of Linear Reaction Diffusion Equation using Modulating Functions

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