Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G8796621621
OpenAlex ID: W7214084832