Traffic Congestion Control on Aw-Rascle-Zhang Model: Full-State Feedback

Abstract

This paper develops boundary feedback control to reduce stop-and-go oscillations in congested traffic regime. The macroscopic traffic dynamics are governed by Aw-Rascle-Zhang(ARZ) model, consisting of second-order, nonlinear partial differential equations(PDEs). The criterion to distinguish free and congested regimes is proposed for the ARZ traffic model, leading to the study of hetero-directional hyperbolic PDE control of congested traffic regime. To stabilize the oscillations of traffic density and speed in a freeway segment, the boundary input through ramp metering is considered. We solve boundary control problems for freeway segment upstream and downstream of the ramp. A general boundary control model is proposed for both control problems. We then design a straight-forward boundary control law to stabilize the downstream of the ramp metering. For the more challenging upstream control problem, we develop a full-state feedback control law through backstepping transformation. The exponential stability in $L^{2}$ sense and finite time convergence to equilibrium are achieved and validated with simulation. The key novelty of this paper is to design both upstream and downstream ramp metering boundary control for congested traffic regime.