Model Predictive Control of Gas Networks Based on Port‐Hamiltonian Formulations

Authors

Andres Ortegón‐Villacorte, Jan Rohleff

Abstract

To efficiently compute optimal compressor actions in gas networks, we investigate port‐Hamiltonian models consisting of linear and a nonlinear model assumptions. The control actions are derived via adjoint‐based gradients that incorporate the constraints of the underlying optimization problem. We then present results from the implementation of a model predictive control (MPC) strategy. We compare the results of the optimization on different models and focus on the computational efficiency. These actions are then validated and periodically updated based on a physically detailed nonlinear model, which captures the detailed system dynamics. This design is applied to a daily demand profile in a network with multiple consumers and sources.

Citation

• Journal: Proceedings in Applied Mathematics and Mechanics
• Year: 2026
• Volume: 26
• Issue: 3
• Pages:
• Publisher: Wiley
• DOI: 10.1002/pamm.70176

BibTeX

@article{Orteg_n_Villacorte_2026,
  title={{Model Predictive Control of Gas Networks Based on Port‐Hamiltonian Formulations}},
  volume={26},
  ISSN={1617-7061},
  DOI={10.1002/pamm.70176},
  number={3},
  journal={Proceedings in Applied Mathematics and Mechanics},
  publisher={Wiley},
  author={Ortegón‐Villacorte, Andres and Rohleff, Jan},
  year={2026}
}

Download the bib file

References

• Aalto H (2015) Model Predictive Control of Natural Gas Pipeline Systems - a case for Constrained System Identification. IFAC-PapersOnLine 48(30):197–202. https://doi.org/10.1016/j.ifacol.2015.12.37 – 10.1016/j.ifacol.2015.12.377
• Koch T, Hiller B, Pfetsch ME, Schewe L (eds) (2015) Evaluating Gas Network Capacitie – 10.1137/1.9781611973693
• Domschke P, Kolb O, Lang J (2022) Fast and reliable transient simulation and continuous optimization of large-scale gas networks. Math Meth Oper Res 95(3):475–501. https://doi.org/10.1007/s00186-021-00765- – 10.1007/s00186-021-00765-7
• T.Breiten P.Domschke J.Giesselmann et al. “A Catalog of Gas Network Models: Pdes Coupling Conditions and Numerical Schemes ” (2026).
• C.O’Malley D.Kourounis G.Hug andO.Schenk “Optimizing Gas Networks Using Adjoint Gradients ” preprint arXiv:1804.09601 (2018).
• Domschke P, Kolb O, Lang J (2015) Adjoint-based error control for the simulation and optimization of gas and water supply networks. Applied Mathematics and Computation 259:1003–1018. https://doi.org/10.1016/j.amc.2015.03.02 – 10.1016/j.amc.2015.03.029
• Herty M, Sachers V (2007) Adjoint calculus for optimization of gas networks. Networks & Heterogeneous Media 2(4):733–750. https://doi.org/10.3934/nhm.2007.2.73 – 10.3934/nhm.2007.2.733
• Fazeny A, Burger M, Pietschmann J-F (2025) Optimal transport on gas networks. Eur J Appl Math 37(3):553–585. https://doi.org/10.1017/s095679252500005 – 10.1017/s0956792525000051
• Gugat M, Habermann J, Hintermüller M, Huber O (2023) Constrained exact boundary controllability of a semilinear model for pipeline gas flow. Eur J Appl Math 34(3):532–553. https://doi.org/10.1017/s095679252200038 – 10.1017/s0956792522000389
• N.Stahl “State Reconstruction of Gas Pipeline Networks ” (Ph.D. dissertation Univeristät Trier 2023).
• Himpe C, Grundel S, Benner P (2021) Model order reduction for gas and energy networks. JMathIndustry 11(1). https://doi.org/10.1186/s13362-021-00109- – 10.1186/s13362-021-00109-4
• Liljegren-Sailer B, Marheineke N (2022) On Snapshot-Based Model Reduction Under Compatibility Conditions for a Nonlinear Flow Problem on Networks. J Sci Comput 92(2). https://doi.org/10.1007/s10915-022-01901- – 10.1007/s10915-022-01901-z
• Egger H, Kugler T, Liljegren-Sailer B, Marheineke N, Mehrmann V (2018) On Structure-Preserving Model Reduction for Damped Wave Propagation in Transport Networks. SIAM J Sci Comput 40(1):A331–A365. https://doi.org/10.1137/17m112530 – 10.1137/17m1125303
• S.Banholzer D.Beermann L.Mechelli andS.Volkwein “POD Suboptimal Control of Evolution Problems: Theory and Applications ” preprint arXiv:2404.07015 (2024).
• J. S.Jehle “First‐Order Augmented Lagrangian Methods for State Constraint Problems ” (Master’s thesis Universität Konstanz 2018).
• M.Lemke “Adjoint Based Data Assimilation in Compressible Flows With Application to Pressure Determination From PIV data ” (PhD dissertation Univeristät Konstanz 2015).
• Nocedal J., Numerical Optimization (2006)
• Osiadacz AJ, Gburzyńska M (2022) Selected Mathematical Models Describing Flow in Gas Pipelines. Energies 15(2):478. https://doi.org/10.3390/en1502047 – 10.3390/en15020478