Delay-Compensated Distributed PDE Control of Traffic with Connected/Automated Vehicles

TL;DR

This paper presents a delay-compensated control method for stabilizing a hyperbolic PDE traffic model with connected vehicles, improving traffic flow stability despite communication delays.

Contribution

It introduces a novel three-branch backstepping transformation with explicit kernels for delay compensation in a PDE traffic model, providing an explicit predictor-feedback controller.

Findings

Proves exponential stability of the delay-compensated system.

Derives explicit inverse transformation for control design.

Demonstrates performance improvements via simulation.

Abstract

We develop an input delay-compensating design for stabilization of an Aw-Rascle-Zhang (ARZ) traffic model in congested regime which is governed by a $2\times 2$ first-order hyperbolic nonlinear PDE. The traffic flow consists of both adaptive cruise control-equipped (ACC-equipped) and manually-driven vehicles. The control input is the time gap of ACC-equipped and connected vehicles, which is subject to delays resulting from communication lag. For the linearized system, a novel three-branch bakcstepping transformation with explicit kernel functions is introduced to compensate the input delay. The transformation is proved {\ae}to be bounded, continuous and invertible, with explicit inverse transformation derived. Based on the transformation, we obtain the explicit predictor-feedback controller. We prove exponential stability of the closed-loop system with the delay compensator in $L_2$ norm. The performance improvement of the closed-loop system under the proposed controller is illustrated in simulation.