Interpretable control rules derived from model predictive control for real-time control in stormwater management

Abstract

Real-time control of stormwater systems improves flood resilience, yet optimization-based methods, such as model predictive control (MPC), remain difficult to implement due to high computational demands and limited operational transparency. As a result, cities continue to rely on rule-based control (RBC), despite the lack of standardized approaches for deriving effective rule sets. This study introduces a framework that formulates interpretable, near-optimal control rules by learning directly from optimal behavior using regression decision trees. MPC is applied offline to generate optimal gate trajectories for 1158 historical rainfall events from 2007 to 2025, which are used to train decision-tree models that extract if-then rules reproducing optimal logic in real time without online optimization. The framework is applied on a basin where the objective is to maintain water levels between 14.8 m and 15.4 m to prevent overflows and preserve recreational activities. Results show that the derived RBC performs better than baseline static control and achieves performance comparable to MPC. In terms of safety, defined by the number of events during which the maximal water level was exceeded, RBC retained 86% of MPC performance, with a total exceedance duration 23% longer, and an increase of 21% in total overflow volume, while reducing gate movement by 57% and computational time by 88%. The extracted rules provided an interpretable representation of optimal control logic, enabling operator understanding, validation, and adjustment. By combining MPC optimization with the transparency and operational simplicity of RBC, this study offers a framework for implementing near-optimal real-time control in stormwater systems.