Stability of discrete-time feed-forward neural networks in NARX configuration

Abstract

The idea of using Feed-Forward Neural Networks (FFNNs) as regression functions for Nonlinear AutoRegressive eXogenous (NARX) models, leading to models herein named Neural NARXs (NNARXs), has been quite popular in the early days of machine learning applied to nonlinear system identification, owing to their simple structure and ease of application to control design. Nonetheless, few theoretical results are available concerning the stability properties of these models. In this paper we address this problem, providing a sufficient condition under which NNARX models are guaranteed to enjoy the Input-to-State Stability (ISS) and the Incremental Input-to-State Stability (δISS) properties. This condition, which is an inequality on the weights of the underlying FFNN, can be enforced during the training procedure to ensure the stability of the model. The proposed model, along with this stability condition, are tested on the pH neutralization process benchmark, showing satisfactory results.

arXiv commentCopyright 2021 by the authors. This work has been accepted to IFAC (19th IFAC Symposium on System Identification: learning models for decision and control) for publication under a Creative Commons Licence CC-BY-NC-ND. Published article: https://doi.org/10.1016/j.ifacol.2021.08.417

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Cited by in corpus (6)

• On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments
• Physics-guided neural networks for feedforward control with input-to-state stability guarantees
• Recurrent Neural Network-based Internal Model Control design for stable nonlinear systems
• An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX models
• Towards lifelong learning of Recurrent Neural Networks for control design
• Robust offset-free nonlinear model predictive control for systems learned by neural nonlinear autoregressive exogenous models