  This paper aims to discuss and analyze the potentialities of Recurrent Neural
Networks (RNN) in control design applications. The main families of RNN are
considered, namely Neural Nonlinear AutoRegressive eXogenous, (NNARX), Echo
State Networks (ESN), Long Short Term Memory (LSTM), and Gated Recurrent Units
(GRU). The goal is twofold. Firstly, to survey recent results concerning the
training of RNN that enjoy Input-to-State Stability (ISS) and Incremental
Input-to-State Stability ($\delta$ISS) guarantees. Secondly, to discuss the
issues that still hinder the widespread use of RNN for control, namely their
robustness, verifiability, and interpretability. The former properties are
related to the so-called generalization capabilities of the networks, i.e.
their consistency with the underlying real plants, even in presence of unseen
or perturbed input trajectories. The latter is instead related to the
possibility of providing a clear formal connection between the RNN model and
the plant. In this context, we illustrate how ISS and $\delta$ISS represent a
significant step towards the robustness and verifiability of the RNN models,
while the requirement of interpretability paves the way to the use of
physics-based networks. The design of model predictive controllers with RNN as
plant's model is also briefly discussed. Lastly, some of the main topics of the
paper are illustrated on a simulated chemical system.
