Geodesic
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

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/cocv/2009035
Classification : 76N25, 35L50, 93C20
Keywords: 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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :