A Linear MPC based on Data-Driven Soil Moisture Level Modelling for Smart Irrigation

Efficient irrigation management is becoming essential to reduce water consumption and operational costs in modern agriculture. This paper proposes a soil moisture level and rainfall volume dynamics identification from historical real data through an autoregressive with exogenous inputs (ARX) model. The identified model is incorporated within an economic Model Predictive Control (MPC) framework that minimizes water consumption costs and time-varying pumping energy costs, while guaranteeing maximum water capacity and minimum soil moisture level constraints for each cultivated subarea. The proposed framework is tested using real data from a smart irrigation system in Paraguay. Numerical results show that the MPC controller exploits low pumping energy cost hours to increase pumping water in advance and reduce it during expensive hours. Compared with a greedy threshold-based irrigation strategy that activates irrigation when the soil moisture level reaches its minimum threshold, the proposed MPC controller achieves a 3.2% reduction in cumulative operating costs, highlighting the benefits of predictive optimization for sustainable and precision agriculture. Furthermore, the use of a linear ARX-based model leads to a convex optimization problem, ensuring global optimality and low computational complexity, thereby making the proposed framework suitable for real-time implementation in precision agriculture.