Robust Constrained Model Predictive Control of Irrigation Systems Based on Data-Driven Uncertainty Set Constructions

We propose a novel data-driven robust model predictive control (RMPC) approach for irrigation system operations, where uncertainty in evapotranspiration and precipitation forecast is explicitly taken into account. A data-driven uncertainty set is constructed to describe the distribution of evapotranspiration forecast error. Meanwhile, the distribution of precipitation forecast error data is analyzed in detail, which is shown to directly rely on forecast values and manifest a time-varying characteristics. To address this issue, we devise a tailored data-driven conditional uncertainty set to disentangle the dependence of distribution of forecast error on forecast values. The generalized affine decision rule is employed to yield a tractable approximation to the optimal control problem. Case studies based on real-world data show that, by effectively utilizing information within historical uncertainty data, the proposed data-driven RMPC approach can help maintaining the soil moisture above the safety level with less water consumptions than traditional control strategies.