Tube-based Robust Model Predictive Control for Pressurized Water Distribution Networks

This paper investigates a tube-based robust economic model predictive control (EMPC) strategy for pressurized water distribution networks (WDNs) with unknown but bounded demand disturbances. The proposed EMPC framework aims to optimize the operation of water storage tanks by scheduling their filling and emptying through pumps and valves while considering both the time-varying electricity tariff and the daily water demands. To handle demand uncertainties, the controller introduces a selection matrix, whose elements indicate whether each actuator participates in disturbance mitigation. The upper and lower bounds of the tightened constraints are precomputed based on known disturbance bounds. During online execution, the robust EMPC employs the nominal system model and simultaneously determines the optimal actuator scheduling. Meanwhile, constraint tightening is applied over the prediction horizon to ensure robust feasibility under uncertainty. Finally, the effectiveness of the proposed strategy is demonstrated through simulation results conducted on a case study.