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

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