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.

在这项工作中，我们提出了一个数据驱动的鲁棒模型预测控制（DDRMPC）框架，该框架利用茎水势（SWP）作为有效控制高附加值作物的基础。通过线性化和离散化水动力学的非线性动力学模型，我们开发了一种状态空间模型，该模型可以预测SWP的动态状态。在模型中，土壤，根和茎是描述系统当前水状况的三个部分。此外，蒸散和降水分别是驱动力和进水口。制定了鲁棒的最佳控制问题，以将SWP维持在安全水平以上，以避免对农作物造成不利影响。为了描述蒸散和降水的预测误差内的不确定性，采用了一种数据驱动的方法，在约束满足和节水之间实现了理想的折衷。同时，表明所提出的DDRMPC确保了可行性和稳定性。进行了基于杏仁树的案例研究，以展示DDRMPC策略相对于开-关控制，确定性等效MPC和鲁棒MPC的有效性。特别是，与开-关控制相比，通过DDRMPC控制树茎水势可将水消耗减少7.9％，同时保持零约束违反的可能性。