Some remarks on the Robust Stackelberg controllability for the heat equation with controls on the boundary
V\'ictor Hern\'andez-Santamar\'ia, Liliana Peralta
TL;DR
This paper investigates robust Stackelberg controllability for the heat equation, introducing hierarchical boundary control strategies that enhance previous results and discuss boundary control placement limitations.
Contribution
It advances the understanding of hierarchical boundary control for the heat equation by incorporating robustness and analyzing boundary control placement constraints.
Findings
Improved controllability results with boundary controls on small parts of the boundary.
Development of a Stackelberg strategy combining controllability and robustness.
Discussion on the feasibility of boundary placement of all controls.
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.
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Some remarks on the Robust Stackelberg controllability for the heat equation with controls on the boundary
Víctor Hernández-Santamaría Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France. E-mail: [email protected]
Liliana Peralta Centro de Investigación en Matemáticas, UAEH, Carretera Pachuca-Tulancingo km 4.5 Pachuca, Hidalgo 42184, Mexico E-mail: [email protected]