Urged by a close future perspective of a traffic flow made of a mix of human-driven vehicles and connected, automated vehicles (CAVs), research has recently focused at making the most of CAVs capabilities to mitigate the instability of the whole, i.e. mixed, traffic flow. In all works, however, either the two sub-flows are studied under a simplifying but unrealistic assumption of flow homogeneity, or drivers’ and vehicles heterogeneity is not correctly taken into account within each sub-flow. We show here that the only condition developed so far to study a car-following model string stability for a heterogeneous flow, is inaccurate. Therefore, we propose a methodology to model string stability that considers drivers’ and vehicles heterogeneity, which is the essence of a real traffic. Uncertain transfer functions are introduced to map the probability distributions of car-following model parameters into a ${\mathcal{L}}_2$ stability measure of a mixed and heterogeneous traffic. Specifically, they allow us to move from the stability analysis of a car-following model, or of a controller, to the stability analysis of a traffic flow, as interpreted by that model, or controller. Eventually, several other theoretical contributions on stability analysis are given in the paper, aiming at reconciling approaches from different fields. Among these, a mathematical justification of the equivalence between the asymptotic stability of a closed-loop platoon system – which has been studied through the famous “traffic wave ansatz” on a ring-road – and the ${\mathcal{L}}_2$ stability of an open-loop platoon system.

受人类驱动车辆和联网的自动驾驶汽车（CAV）混合使用的交通流的不久将来的影响，研究最近集中在充分利用CAV的功能来减轻整体（即混合动力）的不稳定性，交通流。但是，在所有工作中，要么在简化但不切实际的流动同质性假设下研究两个子流，要么在每个子流中未正确考虑驾驶员和车辆的异质性。我们在这里表明，到目前为止，开发用于研究非均质流的汽车跟随模型字符串稳定性的唯一条件是不准确的。因此，我们提出了一种考虑驾驶员和车辆异质性的字符串稳定性建模方法，这是真实点击量的本质。引入不确定的传递函数以将跟车模型参数的概率分布映射到${\mathcal{大号}}_2$混合和异构流量的稳定性度量。具体而言，它们使我们能够从跟车模型或控制器的稳定性分析转到由该模型或控制器解释的交通流的稳定性分析。最终，本文针对稳定性分析提出了其他一些理论性贡献，旨在调和来自不同领域的方法。其中，通过闭环排系统的渐近稳定性（已经通过环形道路上著名的“交通波ansatz”进行了研究）与等价线之间的等价关系进行了数学证明。${\mathcal{大号}}_2$ 开环排系统的稳定性。