Some remarks on the Robust Stackelberg controllability for the heat equation with controls on the boundary

Abstract

In this paper, we present some controllability results for the heat equation in the framework of hierarchic control. We present a Stackelberg strategy combining the concept of controllability with robustness: the main control (the leader) is in charge of a null-controllability objective while a secondary control (the follower) solves a robust control problem, this is, we look for an optimal control in the presence of the worst disturbance. We improve previous results by considering that either the leader or follower control acts on a small part of the boundary. We also present a discussion about the possibility and limitations of placing all the involved controls on the boundary.

Stackelberg exact controllability of a class of nonlocal parabolic equations

“…In that paper, the authors dealt with the Stackelberg-Nash exact controllability of parabolic equations with the possibility of the leader and the followers being placed on the boundary. In [16], the authors extend and discuss the results concerning the robust hierarchic strategy for the heat equation using boundary controls. Recently, the authors in [5] considered a multi-objective control problem for the Kuramoto-Sivashinsky equation with a distributed control called leader and two boundary controls called followers.…”