We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a network. A notion of viscosity solution of Hamilton–Jacobi equations on the network has been proposed in earlier articles. Here, we propose a simple proof of a comparison principle based on arguments from the theory of optimal control. We also discuss stability of viscosity solutions.
DOI : 10.1051/cocv/2014054
Mots-clés : Optimal control, networks, Hamilton–Jacobi equations, viscosity solutions
@article{COCV_2015__21_3_876_0,
author = {Achdou, Yves and Oudet, Salom\'e and Tchou, Nicoletta},
title = {Hamilton{\textendash}Jacobi equations for optimal control on junctions and networks},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {876--899},
publisher = {EDP-Sciences},
volume = {21},
number = {3},
year = {2015},
doi = {10.1051/cocv/2014054},
zbl = {1318.49049},
mrnumber = {3358634},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014054/}
}
TY - JOUR AU - Achdou, Yves AU - Oudet, Salomé AU - Tchou, Nicoletta TI - Hamilton–Jacobi equations for optimal control on junctions and networks JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 876 EP - 899 VL - 21 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014054/ DO - 10.1051/cocv/2014054 LA - en ID - COCV_2015__21_3_876_0 ER -
%0 Journal Article %A Achdou, Yves %A Oudet, Salomé %A Tchou, Nicoletta %T Hamilton–Jacobi equations for optimal control on junctions and networks %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 876-899 %V 21 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014054/ %R 10.1051/cocv/2014054 %G en %F COCV_2015__21_3_876_0
Achdou, Yves; Oudet, Salomé; Tchou, Nicoletta. Hamilton–Jacobi equations for optimal control on junctions and networks. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 876-899. doi : 10.1051/cocv/2014054. http://www.numdam.org/articles/10.1051/cocv/2014054/
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