A biological resource is a population characterized by birth, aging and death, grown in order to produce a profit. The evolution of this system is described by a structured population model, modified to take into account the selection for reproduction or for the market. This selection is the control that has to be optimized in order to maximize the profit. First we prove the well posedness of the descriptive model. Then, the profit is shown to be Gâteaux differentiable with respect to the controls. Finally, we ensure that the maximal profit can be reached by means of Bang–Bang controls.
Accepté le :
DOI : 10.1051/cocv/2016027
Mots-clés : Conservation Laws, optimal control problems, management of biological resources, structured population dynamics
@article{COCV_2017__23_3_1073_0,
author = {Colombo, Rinaldo M. and Garavello, Mauro},
title = {Control of biological resources on graphs},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1073--1097},
publisher = {EDP-Sciences},
volume = {23},
number = {3},
year = {2017},
doi = {10.1051/cocv/2016027},
mrnumber = {3660460},
zbl = {1372.35306},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2016027/}
}
TY - JOUR AU - Colombo, Rinaldo M. AU - Garavello, Mauro TI - Control of biological resources on graphs JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1073 EP - 1097 VL - 23 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016027/ DO - 10.1051/cocv/2016027 LA - en ID - COCV_2017__23_3_1073_0 ER -
%0 Journal Article %A Colombo, Rinaldo M. %A Garavello, Mauro %T Control of biological resources on graphs %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1073-1097 %V 23 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016027/ %R 10.1051/cocv/2016027 %G en %F COCV_2017__23_3_1073_0
Colombo, Rinaldo M.; Garavello, Mauro. Control of biological resources on graphs. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1073-1097. doi : 10.1051/cocv/2016027. http://archive.numdam.org/articles/10.1051/cocv/2016027/
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