Internal Model Control design for systems learned by Control Affine Neural Nonlinear Autoregressive Exogenous Models

TL;DR

This paper introduces a control-affine neural autoregressive model for nonlinear systems, demonstrating improved modeling accuracy and stable control design with lower computational costs on a benchmark system.

Contribution

It proposes a novel CA-NNARX model with stability guarantees and integrates it into a stable IMC scheme, outperforming standard models and controllers in accuracy and efficiency.

Findings

CA-NNARX outperforms standard NNARX in modeling accuracy.

The IMC scheme achieves comparable performance to MPC.

Model stability enhances closed-loop control performance.

Abstract

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 real 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, (ii) the proposed IMC law provides performance comparable to the ones of a standard Model Predictive Controller (MPC) at a significantly lower computational burden, and (iii) the $\delta$ISS of the model is beneficial to the closed-loop performance.