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