Enhancing the robustness of deep reinforcement learning-based real-time control for urban drainage systems through error correction.

Deep reinforcement learning (DRL) has shown strong potential for real-time control (RTC) of urban drainage systems, yet its reliability under practical observation and control uncertainties remains insufficiently understood. This study developed an uncertainty-aware DRL-based RTC framework to systematically quantify the impacts of state observation errors and action execution errors, and to enhance robustness through an auxiliary error-correction mechanism. A primary agent was coupled with a SWMM-based hydraulic model to coordinate three distributed stormwater storage facilities, and Monte Carlo simulations were conducted under multiple rainfall scenarios. Both uncertainty sources degraded RTC performance, with underestimated states and under-executed actions causing substantially greater deterioration than overestimated states or over-executed actions. In the investigated case, under-executed actions increased the flooding percentage change (ΔFPC) by up to 120%, whereas severe state underestimation caused increases of about 30%. Combined-error analysis further revealed a case-specific partial compensation effect between the two uncertainty channels within a certain disturbance range. Based on this finding, an error-correction agent was developed to adjust the actions generated by the primary agent when state observations were underestimated. Validation using four historical rainfall events and two design rainfall events showed that the proposed dual-agent framework reduced mean ΔFPC by up to 51.0% and maximum ΔFPC by up to 36.6% in most scenarios, while also reducing performance variability. Overall, the results demonstrate that simulation-based uncertainty-aware correction can improve the robustness and stability of DRL-based RTC for urban drainage systems under disturbed observations and action execution uncertainty.