PDE-Based Feedback Control of Freeway Traffic Flow via Time-Gap Manipulation of ACC-Equipped Vehicles

We develop a control design for stabilization of traffic flow in the congested regime, based on an Aw-Rascle-Zhang-type (ARZ-type) partial differential equation (PDE) model, for traffic consisting of both adaptive cruise control-equipped (ACC-equipped) and manual vehicles. The control input is the value of the time-gap setting of ACC-equipped and connected vehicles, which gives rise to a problem of control of a $2\times 2$ nonlinear system of the first-order hyperbolic PDEs with in-domain actuation. The feedback law is designed in order to stabilize the linearized system, around a uniform, congested equilibrium profile. The stability of the closed-loop system under the developed control law is shown in constructing a Lyapunov functional. Convective stability is also proved to adopt an input-output approach. The performance improvement of the closed-loop system under the proposed strategy is illustrated in simulation, also employing three different metrics, which quantifies the performance in terms of fuel consumption, total travel time, and comfort.