We investigate a state estimation problem for an infinite dimensional system appearing inpopulation dynamics. More precisely, given a linear model for age-structured populations with spatialdiffusion, we assume the initial distribution to be unknown and that we have at our disposal anobservation locally distributed in both age and space. Using Luenberger observers, we solve the inverseproblem of recovering asymptotically in time the distribution of population. The observer is designedusing a finite dimensional stabilizing output injection operator, yielding an effective reconstructionmethod. Numerical experiments are provided showing the feasibility of the proposed reconstructionmethod.
Accepté le :
DOI : 10.1051/m2an/2016002
Keywords: Inverse problems, observers, stabilization, population dynamics, spatial diffusion
Ramdani, Karim 1 ; Tucsnak, Marius 2 ; Valein, Julie 2
@article{M2AN_2016__50_6_1731_0,
author = {Ramdani, Karim and Tucsnak, Marius and Valein, Julie},
title = {Detectability and state estimation for linear age-structured population diffusion models},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1731--1761},
year = {2016},
publisher = {EDP Sciences},
volume = {50},
number = {6},
doi = {10.1051/m2an/2016002},
zbl = {1353.92084},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2016002/}
}
TY - JOUR AU - Ramdani, Karim AU - Tucsnak, Marius AU - Valein, Julie TI - Detectability and state estimation for linear age-structured population diffusion models JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1731 EP - 1761 VL - 50 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2016002/ DO - 10.1051/m2an/2016002 LA - en ID - M2AN_2016__50_6_1731_0 ER -
%0 Journal Article %A Ramdani, Karim %A Tucsnak, Marius %A Valein, Julie %T Detectability and state estimation for linear age-structured population diffusion models %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1731-1761 %V 50 %N 6 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2016002/ %R 10.1051/m2an/2016002 %G en %F M2AN_2016__50_6_1731_0
Ramdani, Karim; Tucsnak, Marius; Valein, Julie. Detectability and state estimation for linear age-structured population diffusion models. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1731-1761. doi: 10.1051/m2an/2016002
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