Robust Stackelberg controllability for a parabolic equation

Abstract

The aim of this paper is to perform a Stackelberg strategy to control parabolic equations. We have one control, \textit{the leader}, that is responsible for a null controllability property; additionally, we have a control \textit{the follower} that solves a robust control objective. That means, that we seek for a saddle point of a cost functional. In this way, the follower control is not sensitive to a broad class of external disturbances. As far as we know, the idea of combining robustness with a Stackelberg strategy is new in literature