Detectability and state estimation for linear age-structured population diffusion models

Ramdani, Karim; Tucsnak, Marius; Valein, Julie

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1731-1761.

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.

Classification : 92D25, 35R30, 93D15, 93B55
Mots clés : Inverse problems, observers, stabilization, population dynamics, spatial diffusion

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