论文标题
NARX配置中离散时间前馈神经网络的稳定性
Stability of discrete-time feed-forward neural networks in NARX configuration
论文作者
论文摘要
使用前馈神经网络（FFNN）作为非线性自回归外源性（NARX）模型的回归函数的想法，导致此处称为Neural Narxs（NNARXS）的模型，在机器学习的早期就非常流行，以适用于非线性系统识别的机器学习，据其简单的结构和对照设计的设计。但是，关于这些模型的稳定性属性，几乎没有理论上的结果。在本文中，我们解决了这个问题，提供了足够的条件，在该条件下保证NNARX模型可以享受输入到州的稳定性（ISS）和增量输入对国家稳定性（ΔISS）属性。这种情况是对基础FFNN权重的不平等，可以在训练过程中执行以确保模型的稳定性。提出的模型以及这种稳定性条件在pH中和过程基准上进行了测试，显示出令人满意的结果。
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.
