Stability of discrete-time feed-forward neural networks in NARX configuration. Issue 7 (2021)

• Record Type: Journal Article
• Authors: Bonassi, Fabio; Farina, Marcello; Scattolini, Riccardo
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 7(2021)
• Page Start: 547
• Page End: 552
• Publication Date: 2021
• Subjects: Neural networks -- Nonlinear System Identification -- Identification for Control -- Input-to-State Stability -- Incremental Input-to-State Stability; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.08.417
• Languages: English
• ISSNs: 2405-8963

Abstract

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.