Existence of classical solutions and feedback stabilization for the flow in gas networks

Martin Gugat; Michaël Herty

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 1, page 28-51
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Gugat, Martin, and Herty, Michaël. "Existence of classical solutions and feedback stabilization for the flow in gas networks." ESAIM: Control, Optimisation and Calculus of Variations 17.1 (2011): 28-51. <http://eudml.org/doc/272957>.

@article{Gugat2011,
abstract = {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.},
author = {Gugat, Martin, Herty, Michaël},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {classical solution; networked hyperbolic systems; gas networks; feedback law; Lyapunov function},
language = {eng},
number = {1},
pages = {28-51},
publisher = {EDP-Sciences},
title = {Existence of classical solutions and feedback stabilization for the flow in gas networks},
url = {http://eudml.org/doc/272957},
volume = {17},
year = {2011},
}

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
PB - EDP-Sciences
VL - 17
IS - 1
SP - 28
EP - 51
AB - 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.
LA - eng
KW - classical solution; networked hyperbolic systems; gas networks; feedback law; Lyapunov function
UR - http://eudml.org/doc/272957
ER -

References

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