A Dimensionality-Reducible Operational Optimal Control for Wastewater Treatment Process

Operational optimal control (OOC) is an essential component of wastewater treatment process (WWTP). The control variables usually are high-dimensional, nonlinear, and strongly coupled, which can easily fail traditional optimization control methods. Mathematically, these operational variables usually are in the unknown low-dimensional space embedded in the high-dimensional space. Therefore, the OOC problem of WWTP can be resolved as an optimization challenge involving low-dimensional space, and the unknown low-dimensional space is presented in the form of a set of controlled variables in a high-dimensional space, which is normal in real-world industries. Here, a dimension-reducible data-driven optimization control framework for WWTP is proposed. Considering the difficulty in elucidating the whole space of set points, a neural network is designed to approximate the constraint relationship between control variables. The search process is based on optimization methods in low-dimensional space embedded into Euclidean spaces. Furthermore, the convergence of the process is ensured via mathematical analysis. Finally, the experimental simulation of wastewater treatment revealed that this approach is effective for an optimal solution in control systems.