Article
New results concerning the hierarchical control of linear and semilinear parabolic equations
Author/s | Calsavara Caretta, Bianca Morelli
Fernández Cara, Enrique Teresa, Luz de Villa, José Antonio |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2022-02-09 |
Deposit Date | 2022-07-01 |
Published in |
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Abstract | This paper deals with the application of multiple strategies to control some parabolic
PDEs. We assume that we can act on the system through a hierarchy of distributed controls: with a
rst control (a follower), we drive ... This paper deals with the application of multiple strategies to control some parabolic PDEs. We assume that we can act on the system through a hierarchy of distributed controls: with a rst control (a follower), we drive the state exactly to zero; then, with an additional control (the leader), we minimize a prescribed cost functional. That means that we invert the roles played by leaders and followers in the recent literature. We study linear and semilinear problems. More precisely, we prove the existence (and uniqueness in the linear case) of a leader-follower couple. Then, we deduce an appropriate optimality system that must be satis ed by the controls and the corresponding state and adjoint states.We also indicate some generalizations to other controls, PDEs and systems. In particular, we establish similar existence and optimality results for hierarchical-biobjective (Pareto-Stackelberg) control problems, where there are two cost functionals and two independent leader controls whose main task is to nd an associated Pareto equilibrium and one common follower in charge of null controllability. |
Citation | Calsavara Caretta, B.M., Fernández Cara, E., Teresa, L.d. y Villa, J.A. (2022). New results concerning the hierarchical control of linear and semilinear parabolic equations. ESAIM: Control, Optimisation and Calculus of Variations, 28, 14-1-14-26. |
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