翻译后的标题：深度长短时记忆网络：稳定性属性和实验验证翻译后的摘要：本研究旨在研究增量输入状态稳定($\delta$ISS)的深度长短时记忆网络(LSTM)在非线性动力系统识别中的应用。我们展示了网络权重的合适充分条件可以用来建立一个训练过程，能够从数据中学习证实-$\delta$ISS LSTM 模型。所提出的方法在一个真实的电子控制制动系统中进行了测试，以从实验数据中识别系统模型。结果显示出令人满意的建模性能。 (Deep Long-Short Term Memory networks: Stability properties and Experimental validation)

翻译：翻译后的标题：深度长短时记忆网络：稳定性属性和实验验证翻译后的摘要：本研究旨在研究增量输入状态稳定($\delta$ISS)的深度长短时记忆网络(LSTM)在非线性动力系统识别中的应用。我们展示了网络权重的合适充分条件可以用来建立一个训练过程，能够从数据中学习证实-$\delta$ISS LSTM 模型。所提出的方法在一个真实的电子控制制动系统中进行了测试，以从实验数据中识别系统模型。结果显示出令人满意的建模性能。

Fabio Bonassi,Alessio La Bella,Giulio Panzani,Marcello Farina,Riccardo Scattolini

from arxiv, This manuscript is an extended version of a paper accepted for the 2023 European Control Conference (ECC'23). Copyright may be transferred without notice, after which this version may no longer be accessible

The aim of this work is to investigate the use of Incrementally Input-to-State Stable ($\delta$ISS) deep Long Short Term Memory networks (LSTMs) for the identification of nonlinear dynamical systems. We show that suitable sufficient conditions on the weights of the network can be leveraged to setup a training procedure able to learn provenly-$\delta$ISS LSTM models from data. The proposed approach is tested on a real brake-by-wire apparatus to identify a model of the system from input-output experimentally collected data. Results show satisfactory modeling performances.

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