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.

Keywords: 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}, zbl = {1210.49027}, mrnumber = {2775191}, 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 DA - 2011/// SP - 155 EP - 177 VL - 17 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009040/ UR - https://zbmath.org/?q=an%3A1210.49027 UR - https://www.ams.org/mathscinet-getitem?mr=2775191 UR - https://doi.org/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 https://doi.org/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, Volume 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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