On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation
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June 2018, 7(2): 247-273. doi: 10.3934/eect.2018012
Robust Stackelberg controllability for linear and semilinear heat equations
Víctor Hernández-Santamaría 1, and Luz de Teresa 2,
Departamento de Control Automático, CINVESTAV-IPN, Apartado Postal 14-740, 0700, México, D.F., México
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 D.F., México
The first author was supported by CONACyT (Mexico) and both authors were supported by project IN102116 of DGAPA, UNAM. (Mexico).
Received May 2017 Revised December 2017 Published May 2018
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.
Keywords: Hierarchic control, controllability to trajectories, robust control, Carleman inequalities.
Mathematics Subject Classification: Primary: 49J20, 93B05; Secondary: 49K35.
Citation: Víctor Hernández-Santamaría, Luz de Teresa. Robust Stackelberg controllability for linear and semilinear heat equations. Evolution Equations & Control Theory, 2018, 7 (2) : 247-273. doi: 10.3934/eect.2018012
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Víctor Hernández-Santamaría Luz de Teresa