Existence of classical solutions and feedback stabilization for the flow in gas networks. (English) Zbl 1429.76090
Summary: 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 \(L^{2}\)-norm.
MSC:
| 76N25 | Flow control and optimization for compressible fluids and gas dynamics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76G25 | General aerodynamics and subsonic flows |
Keywords:
classical solution; networked hyperbolic systems; gas networks; feedback law; Lyapunov functionReferences:
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