发表机构
City University of Hong Kong; Southern University of Science and Technology（香港城市大学; 南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对存在任意大输入延迟的ARZ交通模型，提出基于反步的延迟补偿边界控制器，通过特征区域核函数构造等技术完成镇定，仿真验证了其有效性。
AI 中文摘要
本文研究存在任意大输入延迟时Aw-Rascle-Zhang（ARZ）交通模型的镇定问题。线性化ARZ模型是具有近端反射的2×2双曲型偏微分方程（PDE）系统，结合输入延迟会带来显著的分析挑战。为解决该问题，我们提出一种基于反步（backstepping）的边界控制器，可在此条件下镇定线性化ARZ模型。输入延迟被建模为一个传输PDE，将整个系统重构为3×3双曲型PDE系统。设计了一种反步变换，将原系统映射为稳定的目标系统，从而实现延迟补偿控制器的设计。本工作的一项关键技术贡献是，针对带延迟的双曲型PDE，我们开发了受两个边界约束的核函数的特征区域构造方法，并通过逐次逼近完成证明；另一项贡献是，我们将小增益定理应用于双曲型PDE的输入-状态稳定性（ISS）。提供了两次仿真以说明所提延迟补偿控制器的有效性：一次将其与无补偿控制器进行比较，另一次采用真实交通车辆数据验证其有效性。
英文摘要
This paper addresses the stabilization problem for Aw-Rascle-Zhang (ARZ) traffic model in the presence of an arbitrarily large input delay. The linearized ARZ model is a $2 \times 2$ hyperbolic partial differential equation (PDE) system with proximal reflection, which introduces significant analytical challenges when combined with input delays. To tackle this problem, we propose a backstepping-based boundary controller capable of stabilizing the linearized ARZ model under these conditions. The input delay is modeled as a transport PDE, which reformulates the entire system into a $3 \times 3$ hyperbolic PDE system. A backstepping transformation is designed to map the original system into a stable target system, enabling the design of a delay-compensated controller. A key technical contribution of this work is that for hyperbolic PDEs with delays, we develop a characteristic-region-wise construction for kernel functions subject to two boundary constraints and close the proof via successive approximation. Another contribution is that we utilize the small-gain theorem for input-to-state stability (ISS) of hyperbolic PDEs. Two simulations are provided to illustrate the effectiveness of the proposed delay-compensated controller: one compares it with a controller without compensation, and the other employs real traffic vehicle data to validate its effectiveness.
