A revision of J.-L. Lions’ notion of sentinels

Abstract

We revisit the notion of sentinel introduced by J.-L. Lions [12] considering the case where the observation of the system and control function of the sentinel have their supports in two different open sets. This point of view leads to problems of null-controllability with or without constraints on the control.
This article focuses on the case of parabolic equations although similar developments can be done for other PDE’s.
The main tool used is an observability inequality of Carleman type which is “adapted” to the constraints.