Stability-guaranteed data-driven nonlinear predictive control of water distribution systems

Stability in the operation of water distribution systems (WDSs) is paramount to maintaining efficient and reliable water delivery. Nonlinear model predictive control (NMPC) emerged as a suitable control strategy due to WDSs' inherent nonlinearity and cross-coupling dynamics. However, classical NMPC is formulated under a finite horizon and does not guarantee closed-loop stability. It also relies heavily on intricate model- based dynamics, a cumbersome and time-consuming process for large-scale WDSs. This paper proposes a comprehensive control strategy that employs a data-enabled model identification technique, replacing physics- based models and ensuring stability and recursive feasibility via quasi-infinite horizon NMPC. The main objective of this work is to satisfy the water demand at every time step while guaranteeing astable pressure head and energy-efficient pump operation in the WDS. A complete stability and feasibility analysis of the control strategy is also provided. Extensive simulations validate the proposed method demonstrating (1) data- driven model accuracy with an unseen and noisy dataset exhibiting 0.01% error and (2) optimal WDS operation under nominal and robust conditions, ensuring demand compliance, cost-savings by 8% ($18k annually), and pressure head stability within 5% of the steady-state value.