粗粒度引导对交通流稳定性的综合分析
Integrated Analysis of Coarse-Grained Guidance for Traffic Flow Stability
AI总结：
本文首次建立粗粒度引导与交通流稳定性的直接理论联系，推导充分条件并扩展至人类驾驶行为，为设计更优控制器提供依据。
摘要：
自动驾驶车辆（AV）能够实现更高效、更可持续的交通系统。大量研究表明，控制一小部分自动驾驶车辆可以平滑交通流并缓解交通拥堵。然而，由于安全和成本方面的担忧，在现实系统中部署自动驾驶车辆面临挑战。一种在不久的将来可以实施的可行替代方法是粗粒度引导，即通过每Δ秒更新的实时指令引导人类驾驶员，以稳定交通。虽然先前的理论研究考虑了连续自动驾驶控制的稳定性分析，但本文首次提出了直接关联提供给人类驾驶员的引导与交通流稳定性结果的综合理论分析。将问题置于李雅普诺夫稳定性框架中，本研究推导了具有保持时长Δ的粗粒度引导稳定系统的充分条件，并提供了分析的扩展以纳入额外的人类驾驶行为，如幅度误差和反应延迟。数值模拟表明，理论分析与模拟结果紧密匹配。该分析进一步提供了关于系统参数与稳定性标准之间关系的见解，并可用于设计具有更大最大保持时长的改进控制器。
英文摘要：
Autonomous vehicles (AVs) enable more efficient and sustainable transportation systems. Ample studies have shown that controlling a small fraction of AVs can smooth traffic flow and mitigate traffic congestion. However, deploying AVs in real-world systems poses challenges due to safety and cost concerns. A viable alternative approach that can be implemented in the near future is $\textit{coarse-grained guidance}$, where human drivers are guided by real-time instructions, updated every $Δ$ seconds, to stabilize the traffic. While previous theoretical studies consider stability analysis for continuous AV control, this article presents the first integrated theoretical analysis that directly relates the guidance provided to the human drivers to the traffic flow stability outcome. Casting the problem into the Lyapunov stability framework, this study derives sufficient conditions for coarse-grained guidance with hold length $Δ$ to stabilize the system, and provides extensions of the analysis to incorporate additional human driving behaviors such as magnitude error and reaction delay. Numerical simulations reveal that the theoretical analysis closely matches simulated results. The analysis further offers insights into the relationship between system parameter and stability criteria, and can be leveraged to design improved controllers with greater maximum hold length.
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