Data-Driven Tube-Based Robust Predictive Control for Constrained Wastewater Treatment Process

The wastewater treatment process (WWTP) is characterized by unknown nonlinearity and external disturbances, which complicates the tracking control of dissolved oxygen concentration (DOC) within operational constraints. To address this issue, a data-driven tube-based robust predictive control (DTRPC) strategy is proposed to achieve stable tracking control of DOC and satisfy the system constraints. First, a tube-based robust predictive control (TRPC) strategy is designed to deal with system constraints and external disturbances. Specifically, a nominal controller is designed to ensure that the nominal output accurately tracks the set-point under tightened constraints, while an auxiliary feedback controller is designed to suppress disturbances and restore the nominal performance of the disturbed WWTP. Second, two fuzzy neural network identifiers are employed to provide accurate predictive outputs for the control process, overcoming the challenges of modeling the WWTP with strong nonlinearity and unknown dynamics. Third, the generalized multiplier method is utilized to solve the constrained optimization problem to obtain the nominal control law, and the gradient descent algorithm is used to obtain the auxiliary control law. The implementation of this composite controller ensures the satisfaction of the system constraints and the effective suppression of disturbances. Finally, the feasibility and stability of the proposed DTRPC strategy are guaranteed through rigorous theoretical analysis, and its effectiveness is demonstrated through the simulations on the benchmark simulation model No.1.