Identification of the local changes in age-structured population dynamics with missing initial condition

In this paper, we study an inverse problem consisting of determining the unknown local changes of a population densities independent of the missing initial population age distribution from the knowledge of some measurement in the state. The main idea is to transform the study of the inverse problem into an optimal control problem with incomplete data. To solve this kind of problem, we use the method of no-regret control approximated by a sequence of low-regret control. We show the existence and uniqueness of the sequence of low-regret control, which converges weakly to the unique no-regret control. The local changes are characterized by a coupled optimality system.