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PreprintCC BY 4.0arXiv

Optimal nodal control and the exponential turnpike property for the flow in gas networks

  • Martin Gugat
  • Michael Herty
  • Michael Schuster
  • Yizhou Zhou
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Abstract

We study an optimal boundary control problem for a quasilinear hyperbolic system describing isothermal gas flow in pipelines. The control acts at network nodes and models the action of compressor stations. The system admits non-constant steady states, which are strictly monotone in space. We work in the framework of H2-solutions and consider an optimal control problem that steers the system toward a prescribed steady state. We establish the existence of optimal controls and then prove the exponential turnpike property, showing that optimal trajectories remain exponentially close to the corresponding steady state over most of the time horizon. The analysis relies on a cheap control property obtained via a Lyapunov approach and on a constructed control. Numerical simulations illustrate the theoretical result.

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Cite

BibTeXRIS
BibTeX
@misc{gugat2026optimal,
  title = {{Optimal nodal control and the exponential turnpike property for the flow in gas networks}},
  author = {Martin Gugat and Michael Herty and Michael Schuster and Yizhou Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26572},
  eprint = {2609.26572},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26572},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Optimal nodal control and the exponential turnpike property for the flow in gas networks
AU  - Martin Gugat
AU  - Michael Herty
AU  - Michael Schuster
AU  - Yizhou Zhou
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26572
UR  - https://arxiv.org/abs/2609.26572
AB  - We study an optimal boundary control problem for a quasilinear hyperbolic system describing isothermal gas flow in pipelines. The control acts at network nodes and models the action of compressor stations. The system admits non-constant steady states, which are strictly monotone in space. We work in the framework of H2-solutions and consider an optimal control problem that steers the system toward a prescribed steady state. We establish the existence of optimal controls and then prove the exponential turnpike property, showing that optimal trajectories remain exponentially close to the corresponding steady state over most of the time horizon. The analysis relies on a cheap control property obtained via a Lyapunov approach and on a constructed control. Numerical simulations illustrate the theoretical result.
ER  -