On Recurrent Neural Networks for learning-based control: Recent results and ideas for future developments

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