Abstract
In this article, we apply the notion of hierarchic control on a distributed system in which the state is governed by a parabolic equation. This notion assumes that we have two controls where one will be the Leader and the other, the Follower. The first control is of controllability type subjected to a constraint, while the second expresses that the state does not move too far from a given state. The results are achieved by means of an observability inequality of the Carleman type, which is ‘adapted’ to the constraint.
Acknowledgements
We are grateful to the referees whose careful reading led to an improvement of this article.