Hierarchic control of a linear heat equation with missing data

Tiomela, Romario Gildas Foko; Mophou, Gisèle; N’Guérékata, Gaston M.

doi:10.1002/mma.6391

Cited by 2 publications

(1 citation statement)

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“…The leader solving an approximate controllability problem while the follower solving an optimal control problem. In the past years, many other researchers have used hierarchic control in the sense of Lions (see for instance [11,10,20,25,26,27,30,13]). Recently, the authors in [9,15] used the hierarchic control combining the concept of controllability with robustness.…”

Section: Introductionmentioning

confidence: 99%

Stackelberg exact controllability of a class of nonlocal parabolic equations

Landry¹,

Kenne²

2023

Preprint

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This paper deals with a multi-objective control problem for a class of nonlocal parabolic equations, where the non-locality is expressed through an integral kernel. We present the Stackelberg strategy that combines the concepts of controllability to trajectories with optimal control. The strategy involves two controls: a main control (the leader) and a secondary control (the follower). The leader solves a controllability to trajectories problem which consists to drive the state of the system to a prescribed target at a final time while the follower solves an optimal control problem which consists to minimize a given cost functional. The paper considers two cases: in the first case, both the leader and the follower act in the interior of the domain, and in the second case, the leader acts in the interior of the domain and the follower acts on a small part of the boundary. These results are applied to both linear and nonlinear nonlocal parabolic systems.

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