Geodesic
Stackelberg–Nash exact controllability for linear and semilinear parabolic equations
Araruna, F.D.1 ; Fernández-Cara, E.2  ; Santos, M.C.1, 3
1 Dpto. de Matemática, Universidade Federal da Paraíba, 58051-900 João Pessoa – PB, Brasil
2 Dpto. EDAN and IMUS, University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
3 Dpto. de Matemática, Universidade Federal de Pernambuco, 50740-540 Recife-PE, Brasil
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 835-856

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This paper deals with the application of Stackelberg–Nash strategies to the control of parabolic equations. We assume that we can act on the system through a hierarchy of controls. A first control (the leader) is assumed to choose the policy. Then, a Nash equilibrium pair (corresponding to a noncooperative multiple-objective optimization strategy) is found; this governs the action of the other controls (the followers). The main novelty in this paper is that, this way, we can obtain the exact controllability to a prescribed (but arbitrary) trajectory. We study linear and semilinear problems and, also, problems with pointwise constraints on the followers.

Reçu le :
DOI : 10.1051/cocv/2014052
Classification : 34K35, 49J20, 35K10
Keywords: Controllability, Stackelberg–Nash strategies, Carleman inequalities

Araruna, F.D. 1 ; Fernández-Cara, E. 2 ; Santos, M.C. 1, 3

1 Dpto. de Matemática, Universidade Federal da Paraíba, 58051-900 João Pessoa – PB, Brasil
2 Dpto. EDAN and IMUS, University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
3 Dpto. de Matemática, Universidade Federal de Pernambuco, 50740-540 Recife-PE, Brasil 
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     author = {Araruna, F.D. and Fern\'andez-Cara, E. and Santos, M.C.},
     title = {Stackelberg{\textendash}Nash exact controllability for linear and semilinear parabolic equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {835--856},
     publisher = {EDP-Sciences},
     volume = {21},
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     year = {2015},
     doi = {10.1051/cocv/2014052},
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     zbl = {1319.35280},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014052/}
}
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Araruna, F.D.; Fernández-Cara, E.; Santos, M.C. Stackelberg–Nash exact controllability for linear and semilinear parabolic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 835-856. doi: 10.1051/cocv/2014052

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