# American Institute of Mathematical Sciences

July  2007, 8(1): 107-114. doi: 10.3934/dcdsb.2007.8.107

## For which objective is birth process an optimal feedback in age structured population dynamics?

 1 INRIA Futurs - Bordeaux, Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351, cours de la libération, 33405 TALENCE cedex, France

Received  November 2005 Revised  February 2006 Published  April 2007

We consider the McKendrick linear model for the evolution of an age structured population. Usually the birth rate is given through a linear functional of the present population using the fertility rate. We are investigating the question of the existence of an objective function, depending on the control and some observation of the state, for which the associated optimal control problem using the birth rate as a control would yield the previous relation using the fertility rate as the optimal closed loop form. Then we consider adaption mechanisms that we model by including a desired value of the observation in the objective function. A modified fertility rate is derived.
Citation: Jacques Henry. For which objective is birth process an optimal feedback in age structured population dynamics?. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 107-114. doi: 10.3934/dcdsb.2007.8.107
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