Adverse weather conditions have a significant impairment on the safety, mobility, and efficiency of highway networks. Dense fog is considered the most dangerous within the adverse weather conditions. As to improve the traffic flow throughput and driving safety in dense fog weather condition on highway, this paper uses a mathematical modeling method to study and control the fleet mixed with human-driven vehicles (HDVs) and connected automatic vehicles (CAVs) in dense fog environment on highway based on distributed model predictive control algorithm (DMPC), along with considering the car-following behavior of HDVs driver based on cellular automatic (CA) model. It aims to provide a feasible solution for controlling the mixed flow of HDVs and CAVs more safely, accurately, and stably and then potentially to improve the mobility and efficiency of highway networks in adverse weather conditions, especially in dense fog environment. This paper explores the modeling framework of the fleet management for HDVs and CAVs, including the state space model of CAVs, the car-following model of HDVs, distributed model predictive control for the fleet, and the fleet stability analysis. The state space model is proposed to identify the status of the feet in the global state. The car-following model is proposed to simulate the driver behavior in the fleet in local. The DMPC-based model is proposed to optimize rolling of the fleet. Finally, this paper used the Lyapunov stability principle to analyze and prove the stability of the fleet in dense fog environment. Finally, numerical experiments were performed in MATLAB to verify the effectiveness of the proposed model. The results showed that the proposed fleet control model has the ability of local asymptotic stability and global nonstrict string stability.

中文翻译：

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浓雾环境下高速公路HDV和CAV的车队管理

不利的天气条件会严重损害高速公路网络的安全性，机动性和效率。在不利的天气条件下，浓雾被认为是最危险的。为了提高高速公路浓雾天气条件下的交通流量通过量和行车安全性，本文采用数学建模方法研究和控制了浓雾中混合有人力驱动车辆（HDV）和自动驾驶汽车（CAV）的车队基于分布式模型预测控制算法（DMPC）的高速公路环境，并考虑基于元胞自动（CA）模型的HDV驾驶员的跟车行为。它旨在提供一种可行的解决方案，以更安全，准确地控制HDV和CAV的混合流，稳定，然后有可能在恶劣天气条件下，特别是在浓雾环境中提高公路网的机动性和效率。本文探讨了轻型货车和轻型货车的车队管理建模框架，包括轻型货车的状态空间模型，轻型车的跟车模型，车队的分布式模型预测控制以及车队稳定性分析。提出了状态空间模型来识别全局状态下脚的状态。提出了汽车跟随模型，以模拟本地车队中的驾驶员行为。提出了基于DMPC的模型来优化机队的滚动。最后，本文采用Lyapunov稳定性原理分析并证明了浓雾环境下舰队的稳定性。最后，在MATLAB中进行了数值实验，以验证所提出模型的有效性。结果表明，所提出的舰队控制模型具有局部渐近稳定性和全局非严格弦稳定性。