String stability plays a crucial role in regulating traffic flow, as traffic oscillation can be triggered by string instability in the car-following (CF) behavior. Although studies over the past decades have provided various methods for analyzing string stability of analytical CF models, no studies have focused on neural network (NN) based CF models despite the fact that these models have exhibited remarkable performance in learning realistic driving behavior in the recent literature. This paper fills this gap by proposing a generic theoretical framework for analyzing the string stability of NN-based CF models through an Estimation-Approximation-Derivation-Calculation process (referred to as EADC framework). Within the framework, we first estimate the steady states of NN-based CF models by solving the corresponding optimization model and obtain the smooth approximation of the NN-based models for linearization, based on which the transfer function is constructed. We then derive the general stability criteria for two commonly used classes of NN in CF modeling, i.e., feedforward NN-based CF models with basic input and recurrent NN-based CF models with multi-step historical information. The string stability is thus obtained by calculating the partial derivatives through the automatic differentiation method. As two case studies, we apply the proposed stability analysis framework on two typical NN-based CF models, the Mo-MLP model (Mo et al., 2021) and the Huang-LSTM model (Huang et al., 2018), and obtained the complete consistency between the theoretical results and the simulation results for both models, which demonstrates the soundness of the proposed EADC framework. Moreover, we discuss the applicability of the proposed EADC stability analysis framework in the emerging era of connected and autonomous vehicles and artificial intelligence.

中文翻译：

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基于神经网络的跟车模型的串稳定性：通用分析框架

串稳定性在调节交通流中起着至关重要的作用，因为跟车（CF）行为中的串不稳定可能会引发交通振荡。尽管过去几十年的研究提供了各种方法来分析分析 CF 模型的弦稳定性，但没有研究关注基于神经网络 (NN) 的 CF 模型，尽管这些模型近年来在学习现实驾驶行为方面表现出了显着的性能。文学。本文填补了这一空白，提出了一个通用的理论框架，通过估计-近似-推导-计算过程来分析基于神经网络的 CF 模型的弦稳定性（称为 EADC 框架）。在该框架内，我们首先通过求解相应的优化模型来估计基于神经网络的CF模型的稳态，并获得基于神经网络的模型的平滑近似以进行线性化，在此基础上构建传递函数。然后，我们推导了 CF 建模中两类常用的 NN 类别的一般稳定性标准，即具有基本输入的基于前馈 NN 的 CF 模型和具有多步历史信息的基于循环 NN 的 CF 模型。通过自动微分法计算偏导数即可得到弦稳定性。作为两个案例研究，我们将所提出的稳定性分析框架应用于两种典型的基于神经网络的 CF 模型，Mo-MLP 模型（Mo 等人，2021）和 Huang-LSTM 模型（Huang 等人，2018），并且两个模型的理论结果和仿真结果完全一致，这证明了所提出的 EADC 框架的合理性。此外，我们还讨论了所提出的 EADC 稳定性分析框架在互联自动驾驶汽车和人工智能新兴时代的适用性。