Optimal control for distributed linear systems subjected to null-controllability

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.

Keywords:

• systems governed by PDEs
• null controllability
• Carleman inequalities
• observability inequality
• Hierarchic control
• optimal control

AMS Subject Classifications::

• 35K05
• 35K15
• 35K20
• 49J20
• 93B05

Acknowledgements

We are grateful to the referees whose careful reading led to an improvement of this article.