Control of mixed-autonomy traffic where Human-driven Vehicles (HVs) and Autonomous Vehicles (AVs) coexist on the road has gained increasing attention over the recent decades. This paper addresses the boundary stabilization problem for mixed traffic on freeways. The traffic dynamics are described by uncertain coupled hyperbolic partial differential equations (PDEs) with Markov jumping parameters, which aim to address the distinctive driving strategies between AVs and HVs. Considering that the spacing policies of AVs vary in mixed traffic, the stochastic impact area of AVs is governed by a continuous Markov chain. The interactions between HVs and AVs such as overtaking or lane changing are mainly induced by impact areas. Using backstepping design, we develop a full-state feedback boundary control law to stabilize the deterministic system (nominal system). Applying Lyapunov analysis, we demonstrate that the nominal backstepping control law is able to stabilize the traffic system with Markov jumping parameters, provided the nominal parameters are sufficiently close to the stochastic ones on average. The mean-square exponential stability conditions are derived, and the results are validated by numerical simulations.

中文翻译：

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混合自主交通偏微分方程系统的均方指数稳定性


近几十年来，人类驾驶车辆（HV）和自动驾驶车辆（AV）在道路上共存的混合自主交通控制越来越受到关注。本文解决了高速公路上混合交通的边界稳定问题。交通动态由具有马尔可夫跳跃参数的不确定耦合双曲偏微分方程（PDE）描述，旨在解决自动驾驶汽车和高压汽车之间独特的驾驶策略。考虑到自动驾驶汽车的间距策略在混合流量中有所不同，自动驾驶汽车的随机影响区域由连续的马尔可夫链控制。 HV 和 AV 之间的相互作用（例如超车或变道）主要由碰撞区域引起。使用反步设计，我们开发了全状态反馈边界控制律来稳定确定性系统（标称系统）。应用李亚普诺夫分析，我们证明，只要标称参数足够接近平均随机参数，标称反步控制律就能够稳定具有马尔可夫跳跃参数的交通系统。推导了均方指数稳定性条件，并通过数值模拟验证了结果。