This paper studies an optimal tuning of the boundary controller for a heterogeneous traffic flow model with disturbances in order to alleviate congested traffic. The macroscopic first-order N-class Aw–Rascle traffic model consists of $2N$ hyperbolic partial differential equations. The vehicle size and the driver’s behavior characterize the type of vehicle. There are $m$ positive characteristic velocities and $2N-m$ negative characteristic velocities in the congested traffic after linearizing the model equations around the steady state depending on the spatial variable. By using the backstepping method, a controller implemented by a ramp metering at the inlet boundary is designed for rejecting the disturbances to stabilize the $2N\times 2N$ heterogeneous traffic system. The developed controller in terms of proportional integral control is derived from mapping the original system to a target system with a proportional integral boundary control rejecting the disturbances. The integral input-to-state stability of the target system is proved by using the Lyapunov method. Finally, an optimization problem is established and solved for seeking the optimal tuning of the controller.

本文研究了具有干扰的异构交通流模型的边界控制器的优化调整，以缓解拥堵交通。宏观一阶 N 类 Aw-Rascle 交通模型包括$\mathrm{2个}否$双曲偏微分方程。车辆的大小和驾驶员的行为表征了车辆的类型。有$米$正特征速度和$\mathrm{2个}否-米$在根据空间变量对稳态周围的模型方程进行线性化后，拥堵交通中的负特征速度。通过使用 backstepping 方法，设计了一个由入口边界处的斜坡计量实现的控制器，用于抑制干扰以稳定$\mathrm{2个}否\times \mathrm{2个}否$异构交通系统。在比例积分控制方面开发的控制器是通过将原始系统映射到具有比例积分边界控制的目标系统来抑制干扰的。利用Lyapunov方法证明了目标系统的积分输入状态稳定性。最后，建立并求解优化问题以寻求控制器的最优整定。