Learning state observers for recurrent neural network models

In this paper, we discuss the problem of learning state observers for Recurrent Neural Network (RNN) black-box models of dynamical systems. State observers are indeed key to designing state-feedback control laws, such as nonlinear Model Predictive Control, with satisfactory closed-loop performance. Besides, they can also improve the training procedure of RNN models themselves. Then, we summarize recent developments aimed at jointly learning RNN models and neural network-based state observers, and we propose a new structure based on the recent $S 5$ architecture. We finally test various observer structures on a $\mathbf{p H}$ neutralization process benchmark system, showing the advantages and shortcomings of each architecture.