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

Víctor Hernández-Santamaría; Liliana Peralta

doi:10.3934/dcdsb.2019177

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2020, Volume 25, Issue 1: 161-190. Doi: 10.3934/dcdsb.2019177

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

Víctor Hernández-Santamaría^1, and
Liliana Peralta^2,

1.
Institut de Mathématiques de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France
2.
Centro de Investigación en Matemáticas, UAEH, Carretera Pachuca-Tulancingo km 4.5 Pachuca, Hidalgo 42184, Mexico

Received: November 2018

Revised: February 2019

Early access: July 2019

Published: January 2020

The first author is supported by project IN102116 of DGAPA, UNAM (Mexico)

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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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Mathematics Subject Classification: Primary: 49J20, 93B05, 49K35.

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