Stability of discrete-time feed-forward neural networks in NARX configuration
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Abstract (arXiv)
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.
Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Dec 2020.
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Citing papers per year: 2021: 2; 2022: 2; 2023: 2; 2024: 0; 2025: 2.
8 papers.
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- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systemscited by 5
- 2022An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX modelscited by 2
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validationcited by 1
- 2022Towards lifelong learning of Recurrent Neural Networks for control designcited by 0
- 2025Hybrid Time-Domain Behavior Model Based on Neural Differential Equations and RNNscited by 0
- 2025Lipschitz-Based Robustness Certification for Recurrent Neural Networks via Convex Relaxationcited by 0
- 2025Lipschitz-Based Robustness Certification for Recurrent Neural Networks via Convex Relaxation22 Sep 2025
- 2025Hybrid Time-Domain Behavior Model Based on Neural Differential Equations and RNNs28 Mar 2025
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validation6 Apr 2023
- 2023Deep networks for system identification: a Survey30 Jan 2023
- 2022Towards lifelong learning of Recurrent Neural Networks for control design8 Aug 2022
- 2022An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX models30 Mar 2022
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments26 Nov 2021
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systems10 Aug 2021