Detectability and state estimation for linear age-structured population diffusion models
1 Inria, 54600 Villers-lès-Nancy, France.
2 Université de Lorraine, Institut Élie Cartan de Lorraine, UMR 7502, 54506 Vandœuvre-lès-Nancy, France.
Revised: 4 January 2016
Accepted: 6 January 2016
We investigate a state estimation problem for an infinite dimensional system appearing in population dynamics. More precisely, given a linear model for age-structured populations with spatial diffusion, we assume the initial distribution to be unknown and that we have at our disposal an observation locally distributed in both age and space. Using Luenberger observers, we solve the inverse problem of recovering asymptotically in time the distribution of population. The observer is designed using a finite dimensional stabilizing output injection operator, yielding an effective reconstruction method. Numerical experiments are provided showing the feasibility of the proposed reconstruction method.
Mathematics Subject Classification: 92D25 / 35R30 / 93D15 / 93B55
Key words: Inverse problems / observers / stabilization / population dynamics / spatial diffusion
© EDP Sciences, SMAI 2016