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This work describes a novel Physics-Informed Hybrid Neural Network (PIHNN) model structure based on the Gated Recurrent Unit (GRU) neural network that combines the first principle and black-box data-driven approaches. We recommend the presented modeling method when the measurement of process variables is possible, but only in some limited neighborhood of the operating points, and the available first principle model describing the process is generally correct but not accurate. We discuss three methods of data fusion. Two of them utilize the fuzzy approach, while the third one relies on an additional neural network of the Multi-Layer Perceptron (MLP) type. The first method assumes a simplified data fusion block, while the next two use machine learning to minimize the overall model error. The efficiency of the presented approach and data fusion techniques is demonstrated for a benchmark chemical process (the pH reactor). Finally, we consider applying the PIHNN model in Model Predictive Control (MPC). It gives much better control quality than the MPC controller relying on the entirely black-box GRU model.

• Model Predictive Control (MPC) algorithms for GRU and LSTM networks are described and evaluated for two benchmarks. • It is shown that the typical approach to MPC that hinges on successively linearized networks does not give precise predictions and satisfactory control quality. • The presented MPC control schemes utilize online advanced trajectory linearization, which yields simple quadratic optimization programs. • The discussed approaches give excellent prediction accuracy and control quality. • The performance of MPC based on LSTM and GRU networks is compared; simpler GRU ones are recommended. This article is concerned with Model Predictive Control (MPC) algorithms that use Short Term Memory (LSTM) and Gated Recurrent Unit (GRU) neural networks for prediction. For two benchmark processes, it is shown that the typical approach to MPC that hinges on successively linearized LSTM or GRU models do not give precise predictions and satisfactory control quality. The presented MPC control schemes utilize online advanced trajectory linearization, which yields simple quadratic optimization programs. It is shown that the discussed approaches give excellent prediction accuracy and control quality, very similar to that possible in MPC with full nonlinear prediction and nonlinear optimization done online. It is also demonstrated that the described MPC algorithms are a few times faster than the MPC method with nonlinear optimization. Moreover, the performance of MPC based on LSTM and GRU networks is compared, and simpler GRU networks are recommended. [ABSTRACT FROM AUTHOR]