A new hierarchical control for the wave equation

This work present results on controlling a wave equation with a hierarchy of actions; a leader control acts and the follower reacts to this action trying to get a different target of the one of the leader. In this paper, we invert the roles of the classical Stackelberg strategies where the leader has a controllability target and the follower and optimization objective. See e.g. Lions (1994), Araruna et al. (2018), Araruna et al. (2020). We will consider a leader aiming to minimize a functional and a follower control with an exact controllability target. • This paper treats two hierarchical control problems for the wave equation. • We analyze Stackelberg strategies when the leader control has an optimization objective and the follower one, an exact controllability objective. • We present results when the follower control acts on the boundary and the leader acts in the interior or in the boundary.