  This paper develops output feedback boundary control to mitigate traffic
congestion of a unidirectional two-lane freeway segment. The macroscopic
traffic dynamics are described by the Aw-Rascle-Zhang (ARZ) model respectively
for both the fast and slow lanes. The traffic density and velocity of each of
the two lanes are governed by coupled $2 \times 2$ nonlinear hyperbolic partial
differential equations (PDEs). Lane-changing interactions between the two lanes
lead to exchanging source terms between the two pairs second-order PDEs.
Therefore, we are dealing with $4 \times 4$ nonlinear coupled hyperbolic PDEs.
Based on driver's preference for the slow and fast lanes, a reference system of
lane-specific uniform steady states in congested traffic is chosen. To
stabilize traffic densities and velocities of both lanes to the steady states,
two distinct variable speed limits (VSL) are applied at outlet boundary,
controlling the traffic velocity of each lane. Using backstepping
transformation, we map the coupled heterodirectional hyperbolic PDE system into
a cascade target system, in which traffic oscillations are damped out through
actuation of the velocities at the downstream boundary. Two full-state feedback
boundary control laws are developed. We also design a collocated boundary
observer for state estimation with sensing of densities at the outlet. Output
feedback boundary controllers are obtained by combining the collocated observer
and full-state feedback controllers. The finite time convergence to equilibrium
is achieved for both the controllers and observer designs. Numerical
simulations validate our design in two different traffic scenarios.
