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An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures.
@article{COCV_2003__9__437_0,
author = {Pedregal, Pablo},
title = {Some remarks on existence results for optimal boundary control problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {437--448},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2003021},
mrnumber = {1998709},
zbl = {1066.49005},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003021/}
}
TY - JOUR AU - Pedregal, Pablo TI - Some remarks on existence results for optimal boundary control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2003 SP - 437 EP - 448 VL - 9 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003021/ DO - 10.1051/cocv:2003021 LA - en ID - COCV_2003__9__437_0 ER -
%0 Journal Article %A Pedregal, Pablo %T Some remarks on existence results for optimal boundary control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 437-448 %V 9 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003021/ %R 10.1051/cocv:2003021 %G en %F COCV_2003__9__437_0
Pedregal, Pablo. Some remarks on existence results for optimal boundary control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 437-448. doi: 10.1051/cocv:2003021
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