The data transmission in wastewater treatment processes (WWTPs) depends on wireless networks. However, limited network bandwidth frequently results in data packet losses. Moreover, intermittent sensor faults caused by sludge adhesion and sensor aging can induce probabilistic sampling (PS). These communication constraints degrade control system performance and stability, while external disturbances further complicate dynamics. To address these challenges, a data-driven robust model predictive control (DRMPC) approach is proposed to stabilize WWTPs under communication constraints and external disturbances. First, an equivalent PS (EPS) model is established to characterize the double randomness introduced by communication constraints, including PS and consecutive packet losses (CPLs). Then, based on the EPS model, a two-loop control framework is constructed. Specifically, a nominal model predictive control (MPC) is designed as a nominal control loop to steer the nominal output to the reference trajectory, where a multistep identifier is designed to capture the unknown dynamics of the nominal system. Then, the cost function is formulated by incorporating the expectation of predictive outputs and the variation in control error, which effectively enhances the tracking control capability of the nominal system. Furthermore, a fuzzy neural network (FNN) controller is constructed as a feedback control loop to regulate the error system to mitigate the effect of external disturbances, ensuring that the actual output converges to the nominal output. Finally, a theoretical proof of system stability is provided. Meanwhile, the proposed DRMPC scheme is experimentally validated on the Benchmark Simulation Model No.1 (BSM1) for WWTPs, demonstrating its effectiveness.
Sun et al. (2026) studied this question.