Internal Model Control Design for Systems Learned by Control Affine Neural Nonlinear Autoregressive Exogenous Models

This paper explores the use of Control Affine Neural Nonlinear AutoRegressiveeXogenous (CA-NNARX) models for nonlinear system identification and model-basedcontrol design. The idea behind this architecture is to match the knowncontrol-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, devisingsufficient conditions for their incremental Input-to-State Stability(δISS) that can be enforced at the model training stage. The model'sstability property is then leveraged to design a stable Internal Model Control(IMC) architecture. The proposed control scheme is tested on a simulatedQuadruple Tank benchmark system to address the output reference trackingproblem. The results achieved show that (i) the modeling accuracy of CA-NNARXis superior to the one of a standard NNARX model for given weight size andtraining epochs, and (ii) the proposed IMC law provides performance comparableto the ones of a standard Model Predictive Controller (MPC) at a significantlylower computational burden.