Control of Stackelberg for Coupled Parabolic Equations

We consider the Stackelberg problem for coupled parabolic equations with a finite number of constraints on one of the states. This notion assumes that we have two controls to determine. The first control is supposed to bring the solution of the coupled system subjected to a finite number of constraints at rest at time zero while the second expresses that the states do not move too far from given states. The results are achieved by means of an observability inequality of Carleman adapted to the constraints.