Data-driven predictive control strategies of water distribution systems using sparse regression

Water distribution systems (WDSs) are inherently complex due to the interconnected hydraulic components. Model predictive control (MPC) offers a sophisticated approach to managing WDSs due to its predictive capability and efficacy in handling multivariable constraints. However, MPC's effectiveness is limited by its heavy reliance on accurate dynamic models. This paper presents an innovative control framework for WDSs, integrating data-driven dynamic identification that leverages sparse-regression theory (SR-based ID) with three distinct MPC techniques: 1) linear time-invariant, 2) linear time-varying via successive linearization, 3) and nonlinear MPCs. The proposed comprehensive control framework contributes to developing a data-driven MPC framework for WDSs, eliminating the reliance on the WDSs' physical models. A comparative analysis between the data-driven MPC strategies is provided to identify the most suitable control method for varying scenarios in WDS, balancing computational efficiency with dynamic response and tracking accuracy. The proposed data-driven MPC algorithm has been tested on a quadruple tank system that resembles WDSs' nonlinearity and cross-coupling dynamics. Despite the varying control signals, noisy measurements, and parameter variations, the proposed SRbased ID proved to be robust in capturing the dynamics of the system with forecasting errors as low as 0.29 %. The results further highlight each control method's notable attributes and shortcomings centered on trajectory tracking performance, boasting a low error of 0.02 % and computational benefits featuring fast execution time at 0.04 s. Overall, the findings underscore the high accuracy and robustness of the SR-based MPC algorithms under different operational conditions, offering scalable and adaptable solutions for large-scale water distribution management.