The research theme under investigation concerns the use of Neural Networks for data-driven control of unknown dynamical systems. Neural Networks have proven to be powerful tools for nonlinear system identification and control design, yet little results advocating their use in theoretically-sound contexts are available in the literature.

In this regard, research work has been devoted on the Input-to-State Stability (ISS) and Incremental Input-to-State Stability (𝛿ISS) properties of Recurrent Neural Networks (RNNs). In particular, sufficient conditions have been devised under which the RNN architectures used for identification (such as NARXs, LSTMs and GRUs) are guaranteed to enjoy these properties.

The ISS and 𝛿ISS are useful stability notions for nonlinear systems, which have been leveraged to perform, among other things, the safety verification of the model and to design Model Predictive Control regulators with guaranteed nominal closed-loop stability and recursive feasibility.