  This paper explores the use of Control Affine Neural Nonlinear AutoRegressive
eXogenous (CA-NNARX) models for nonlinear system identification and model-based
control design. The idea behind this architecture is to match the known
control-affine structure of the system to achieve improved performance.
Coherently with recent literature of neural networks for data-driven control,
we first analyze the stability properties of CA-NNARX models, devising
sufficient conditions for their incremental Input-to-State Stability
($\delta$ISS) that can be enforced at the model training stage. The model's
stability property is then leveraged to design a stable Internal Model Control
(IMC) architecture. The proposed control scheme is tested on a simulated
Quadruple Tank benchmark system to address the output reference tracking
problem. The results achieved show that (i) the modeling accuracy of CA-NNARX
is superior to the one of a standard NNARX model for given weight size and
training epochs, and (ii) the proposed IMC law provides performance comparable
to the ones of a standard Model Predictive Controller (MPC) at a significantly
lower computational burden.
