Multistage economic MPC for systems with a cyclic steady state: A gas network case study

Naik, Sakshi [Carnegie Mellon University, Pittsburgh, PA (United States)] (ORCID:000000027155791X); Ghilardi, Lavinia [Politecnico di Milano (Italy)] (ORCID:000000023917103X); Parker, Robert [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)]; Biegler, Lorenz T. [Carnegie Mellon University, Pittsburgh, PA (United States)] (ORCID:0000000338754441)

doi:10.1016/j.ces.2025.122276

DOE OSTI · 2574838

Multistage economic MPC for systems with a cyclic steady state: A gas network case study

Naik, Sakshi [Carnegie Mellon University, Pittsburgh, PA (United States)] (ORCID:000000027155791X)·Ghilardi, Lavinia [Politecnico di Milano (Italy)] (ORCID:000000023917103X)·Parker, Robert [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)]·Biegler, Lorenz T. [Carnegie Mellon University, Pittsburgh, PA (United States)] (ORCID:0000000338754441)

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Abstract

Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. This paper presents a novel multistage economic nonlinear model predictive control (E-NMPC) framework for dynamic systems operating under uncertainty, with specific application to natural gas transmission networks. A key innovation lies in the integration of cyclic steady-state (CSS) constraints within the multistage MPC formulation, enabling the controller to manage periodic operating conditions commonly observed in energy systems. A Lyapunov-based descent condition is enforced to ensure robust stability of the controller. The multistage economic MPC framework is validated on two gas pipeline case studies, where it successfully minimizes net energy consumption, respects operational constraints under uncertain demand profiles, and guides the network to optimal cyclic operation. The Lyapunov function remains bounded in both case studies, validating the robust stability of multistage E-NMPC.

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03 NATURAL GAS 97 MATHEMATICS AND COMPUTING Dynamic optimization Gas network operations Nonlinear control Nonlinear programming Optimization under uncertainty Stochastic optimization

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Naik, Sakshi [Carnegie Mellon University, Pittsburgh, PA (United States)] (ORCID:000000027155791X), Ghilardi, Lavinia [Politecnico di Milano (Italy)] (ORCID:000000023917103X), Parker, Robert [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)], Biegler, Lorenz T. [Carnegie Mellon University, Pittsburgh, PA (United States)] (ORCID:0000000338754441). 2025-07-25. Multistage economic MPC for systems with a cyclic steady state: A gas network case study. https://doi.org/10.1016/j.ces.2025.122276

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