Data-driven robust model predictive control framework for stem water potential regulation and irrigation in water management

In this work, we propose a data-driven robust model predictive control (DDRMPC) framework that utilizes stem water potential (SWP) as a basis for effective irrigation control of high value-added crops. By linearizing and discretizing a nonlinear dynamic model of water dynamics, we develop a state-space model that predicts the dynamic state of SWP. In the model, soil, root, and stem are the three compartments to describe current water status of the system. In addition, evapotranspiration and precipitation are the driving force and the water inlet, respectively. A robust optimal control problem is formulated to maintain SWP above a safe level to avoid detrimental effects on crops. To describe the uncertainty within prediction errors of evapotranspiration and precipitation, a data-driven approach is adopted, which achieves a desirable tradeoff between constraint satisfaction and water saving. Meanwhile, it is shown that the proposed DDRMPC ensures both feasibility and stability. A case study based on almond tree is carried out to showcase the effectiveness of the DDRMPC strategy relative to on-off control, certainty equivalent MPC and robust MPC. In particular, the control of tree stem water potential through DDRMPC can reduce the water consumption by 7.9% compared with on-off control while maintaining zero probability of constraint violation.