Robust hierarchic control for a population dynamics model with missing birth rate

摘要

In this paper, we study the hierarchic control problem for a linear system of a population dynamics model with an unknown birth rate. Using the notion of low-regret control and an adapted observability inequality of Carleman type, we show that there exist two controls such that, the first control called follower solves an optimal control problem which consists in bringing the state of the linear system to the desired state, and the second one named leader is supposed to lead the population to extinction at final time.