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.
DOI : 10.1051/cocv/2014052
Mots-clés : Controllability, Stackelberg–Nash strategies, Carleman inequalities
@article{COCV_2015__21_3_835_0,
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},
number = {3},
year = {2015},
doi = {10.1051/cocv/2014052},
mrnumber = {3358632},
zbl = {1319.35280},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014052/}
}
TY - JOUR AU - Araruna, F.D. AU - Fernández-Cara, E. AU - Santos, M.C. TI - Stackelberg–Nash exact controllability for linear and semilinear parabolic equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 835 EP - 856 VL - 21 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014052/ DO - 10.1051/cocv/2014052 LA - en ID - COCV_2015__21_3_835_0 ER -
%0 Journal Article %A Araruna, F.D. %A Fernández-Cara, E. %A Santos, M.C. %T Stackelberg–Nash exact controllability for linear and semilinear parabolic equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 835-856 %V 21 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014052/ %R 10.1051/cocv/2014052 %G en %F COCV_2015__21_3_835_0
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. http://www.numdam.org/articles/10.1051/cocv/2014052/
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