We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
Mots-clés : optimal control, viscosity solutions, differential games, switching, flow control, networks
@article{COCV_2011__17_1_155_0,
author = {Bagagiolo, Fabio and Bauso, Dario},
title = {Objective function design for robust optimality of linear control under state-constraints and uncertainty},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {155--177},
publisher = {EDP-Sciences},
volume = {17},
number = {1},
year = {2011},
doi = {10.1051/cocv/2009040},
mrnumber = {2775191},
zbl = {1210.49027},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009040/}
}
TY - JOUR AU - Bagagiolo, Fabio AU - Bauso, Dario TI - Objective function design for robust optimality of linear control under state-constraints and uncertainty JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 155 EP - 177 VL - 17 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009040/ DO - 10.1051/cocv/2009040 LA - en ID - COCV_2011__17_1_155_0 ER -
%0 Journal Article %A Bagagiolo, Fabio %A Bauso, Dario %T Objective function design for robust optimality of linear control under state-constraints and uncertainty %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 155-177 %V 17 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009040/ %R 10.1051/cocv/2009040 %G en %F COCV_2011__17_1_155_0
Bagagiolo, Fabio; Bauso, Dario. Objective function design for robust optimality of linear control under state-constraints and uncertainty. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 1, pp. 155-177. doi : 10.1051/cocv/2009040. http://www.numdam.org/articles/10.1051/cocv/2009040/
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