Hierarchic Control for a Two-Stroke Linear System with Missing Data

In this paper, we study a new hierarchical control problem for a linear two-stroke missing data problem, adjoint to an age and space structured single species population dynamics problem. We show that there are two controls such that the first control, called the follower, solves an optimal control problem which consists in bringing the state of the two-stroke linear system to a desired state, and the second control, called the leader, solves a null controllability problem. The results are obtained by means of an observability inequality associated with a homogeneous Dirichlet boundary condition.