A continuous stirred-tank reactor (CSTR) system is widely applied in wastewater treatment processes. Its control is a challenging industrial-process-control problem due to great difficulty to achieve accurate system identification. This work proposes a deep learning-based model predictive control (DeepMPC) to model and control the CSTR system. The proposed DeepMPC consists of a growing deep belief network (GDBN) and an optimal controller. First, GDBN can automatically determine its size with transfer learning to achieve high performance in system identification, and it serves just as a predictive model of a controlled system. The model can accurately approximate the dynamics of the controlled system with a uniformly ultimately bounded error. Second, quadratic optimization is conducted to obtain an optimal controller. This work analyzes the convergence and stability of DeepMPC. Finally, the DeepMPC is used to model and control a second-order CSTR system. In the experiments, DeepMPC shows a better performance in modeling, tracking, and antidisturbance than the other state-of-the-art methods.

Deep belief network (DBN) is an efficient learning model for unknown data representation, especially nonlinear systems. However, it is extremely hard to design a satisfactory DBN with a robust structure because of traditional dense representation. In addition, backpropagation algorithm-based fine-tuning tends to yield poor performance since its ease of being trapped into local optima. In this article, we propose a novel DBN model based on adaptive sparse restricted Boltzmann machines (AS-RBM) and partial least square (PLS) regression fine-tuning, abbreviated as ARP-DBN, to obtain a more robust and accurate model than the existing ones. First, the adaptive learning step size is designed to accelerate an RBM training process, and two regularization terms are introduced into such a process to realize sparse representation. Second, initial weight derived from AS-RBM is further optimized via layer-by-layer PLS modeling starting from the output layer to input one. Third, we present the convergence and stability analysis of the proposed method. Finally, our approach is tested on Mackey-Glass time-series prediction, 2-D function approximation, and unknown system identification. Simulation results demonstrate that it has higher learning accuracy and faster learning speed. It can be used to build a more robust model than the existing ones.

Wastewater treatment processes (WWTPs) have been considered as complex control problems, because effluent water standard, stability and multi-operational conditions need to be taken into account. In this work, an event-driven model predictive control with deep learning (EMPC-DL) is proposed for the control problems to improve the running performance of WWTPs. First, several events are defined based on different operational conditions reflected by operational data. Then, an event-driven deep belief network (EDBN) is developed based on deep learning to approximate the nonlinear characteristics of the WWTPs. Second, a quadratic optimization is designed to solve the control law of MPC based on the predictive output of the EDBN. The major advantage of quadratic optimization is its efficiency, which is achieved by an efficient strategy that only needs one-step prediction of EDBN during one-time rolling optimization. Third, this paper gives convergence and stability analysis of EMPC-DL. Finally, the feasibility and applicability of EMPC-DL are demonstrated on the benchmark simulation model No. 1 (BSM1). The experimental results show that EMPC-DL achieves the more satisfactory performance in modeling, controlling, and tracking water quality parameters than its peers.