Robust Optimal Control for Wastewater Treatment Process With Uncertain Time Delays.

To achieve the excellent operational performance of the wastewater treatment process, optimal control has been considered a reliable method. However, there is a time-delay response of the operation performances to the process variables, leading to uncertainties of operational optimal objectives. It is difficult to obtain the optimal set-points due to the uncertain operational optimal objectives. Therefore, a kernel-density-estimation-based robust optimal control (KDE-ROC) method is proposed. First, a data-driven prediction strategy is developed to construct the uncertain operational optimal objectives. Based on the time-delay intervals, the uncertainties between process variables and operational optimal objectives are expressed. Second, a kernel-density-estimation-based robust optimization algorithm is designed to solve the uncertain operational optimal objectives. Then, the optimal set-points of process variables are obtained depending on the robustness index to reduce the influence of uncertainties. Third, an adaptive neural network controller is developed to track the optimal set-points of process variables. Finally, the proposed KDE-ROC is applied in benchmark simulation model No.1. In the experimental results, the optimal control performance of KDE-ROC is compared with some effective optimal control strategies to demonstrate its effectiveness.