  In this paper we develop a boundary state feedback control law for a traffic
flow network system in its most fundamental form: one incoming and one outgoing
road connected by a junction. The macroscopic traffic dynamics on each road
segment are governed by Aw-Rascle-Zhang (ARZ) model, consisting of second-order
nonlinear partial differential equations (PDEs) for traffic density and
velocity. Different equilibrium road conditions are considered for the
connected segments. For stabilization of the stop-and-go traffic congestion on
the two roads, we consider a ramp metering located at the connecting junction.
The traffic flow rate entering from the on-ramp to the mainline junction is
actuated. The objective is to simultaneously stabilize the upstream and
downstream traffic to a given spatially-uniform constant steady-state. We
design a full state feedback control law for this under-actuated network of two
systems of two hetero-directional linear first-order hyperbolic PDEs
interconnected through the boundary condition (junction). The exponential
stability is validated by numerical simulation.
