The existence of stochastic sampling phenomena in wastewater treatment processes (WWTPs) breaks the assumption that the existing control strategies use periodic data, and the operational constraints of equipment and the requirements for effluent water quality impose constraints on the system's input and output. These factors collectively increase the difficulty of achieving stable control of dissolved oxygen concentration (DOC). To solve these problems, a data-driven model predictive control (DDMPC) strategy is proposed to achieve stable control of constrained WWTPs with stochastic sampling intervals. First, a DDMPC framework is designed, which involves designing the objective function based on the mathematical expectation of the predicted output and considering system input and output constraints. In this framework, the problem of stochastic data acquisition caused by stochastic sampling can be solved, and the stable operation of the system can be ensured under constraints. Second, a data-driven multimodel prediction structure is constructed based on the stochastic characteristics of the sampling intervals. Specifically, fuzzy neural networks (FNNs) that match possible sampling intervals are established, thereby providing predictive outputs for the control process at the corresponding sampling instants. Third, a controller solving algorithm based on the generalized multiplier method is proposed, in which the constrained optimization problem within the model-predictive control (MPC) framework is reformulated by incorporating system constraints into the objective function as penalty functions to obtain the optimal control input that satisfies the constraints. Finally, the stability of the proposed DDMPC strategy is demonstrated, and its effectiveness is verified through the simulations on the benchmark simulation model No. 1 (BSM1). The results show that the proposed DDMPC strategy can achieve stable control of DOC in constrained WWTPs with stochastic sampling intervals.
Sun et al. (2026) studied this question.