We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.
Mots-clés : classical solution, networked hyperbolic systems, gas networks, feedback law, Lyapunov function
@article{COCV_2011__17_1_28_0,
author = {Gugat, Martin and Herty, Micha\"el},
title = {Existence of classical solutions and feedback stabilization for the flow in gas networks},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {28--51},
publisher = {EDP-Sciences},
volume = {17},
number = {1},
year = {2011},
doi = {10.1051/cocv/2009035},
mrnumber = {2775185},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009035/}
}
TY - JOUR AU - Gugat, Martin AU - Herty, Michaël TI - Existence of classical solutions and feedback stabilization for the flow in gas networks JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 28 EP - 51 VL - 17 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009035/ DO - 10.1051/cocv/2009035 LA - en ID - COCV_2011__17_1_28_0 ER -
%0 Journal Article %A Gugat, Martin %A Herty, Michaël %T Existence of classical solutions and feedback stabilization for the flow in gas networks %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 28-51 %V 17 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009035/ %R 10.1051/cocv/2009035 %G en %F COCV_2011__17_1_28_0
Gugat, Martin; Herty, Michaël. Existence of classical solutions and feedback stabilization for the flow in gas networks. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 1, pp. 28-51. doi : 10.1051/cocv/2009035. http://www.numdam.org/articles/10.1051/cocv/2009035/
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