Robust Stackelberg controllability for linear and semilinear heat equations

Víctor Hernández-Santamaría; Luz de Teresa

doi:10.3934/eect.2018012

Article Contents

2018, Volume 7, Issue 2: 247-273. Doi: 10.3934/eect.2018012

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Robust Stackelberg controllability for linear and semilinear heat equations

Víctor Hernández-Santamaría^1, and
Luz de Teresa^2,

1.
Departamento de Control Automático, CINVESTAV-IPN, Apartado Postal 14-740, 0700, México, D.F., México
2.
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 D.F., México

Received: May 2017

Revised: December 2017

Published: May 2018

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Abstract

In this paper, we present a Stackelberg strategy to control a semilinear parabolic equation. We use the concept of hierarchic control to combine the concepts of controllability with robustness. We have a control named the leader which is responsible for a controllability to trajectories objective. Additionally, we have a control named the follower, that solves a robust control problem. That means we solve for the optimal control in the presence of the worst disturbance case. In this way, the follower control is insensitive to a broad class of external disturbances.

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

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References

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