Traffic Congestion Control on Two-lane Aw-Rascle-Zhang Model

Abstract

This paper develops full-state feedback boundary control to reduce two-lane traffic congestion in a freeway segment. The macroscopic traffic dynamics is described by a two-lane Aw-Rascle-Zhang(ARZ) model with lane-changing between a fast and a slow lane. The traffic density and speed of each lane is governed by a coupled second-order, nonlinear hyperbolic partial differential equations(PDEs). Lane-changing interactions lead to exchanging source terms between these two second-order PDEs. We linearize it around a reference system regarding driver's preference over the fast and slow lane. To stabilize the oscillations of traffic densities and speeds in this two-lane problem, two variable speed limits are applied at outlet boundary, controlling the traffic speed of each lane respectively. Using backstepping transformation, we map the coupled hetero-directional hyperbolic system into a cascade target system, in which traffic oscillations can be damped through the actuation of speeds at outlet boundary. Two full-state feedback boundary control laws are developed and the finite time convergence to equilibrium is achieved for the closed-loop system.