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This paper develops output feedback boundary control to mitigate trafficcongestion of a unidirectional two-lane freeway segment. The macroscopictraffic dynamics are described by the Aw-Rascle-Zhang (ARZ) model respectivelyfor both the fast and slow lanes. The traffic density and velocity of each ofthe two lanes are governed by coupled $2 \times 2$ nonlinear hyperbolic partialdifferential equations (PDEs). Lane-changing interactions between the two laneslead 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 oflane-specific uniform steady states in congested traffic is chosen. Tostabilize 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 backsteppingtransformation, we map the coupled heterodirectional hyperbolic PDE system intoa cascade target system, in which traffic oscillations are damped out throughactuation of the velocities at the downstream boundary. Two full-state feedbackboundary control laws are developed. We also design a collocated boundaryobserver for state estimation with sensing of densities at the outlet. Outputfeedback boundary controllers are obtained by combining the collocated observerand full-state feedback controllers. The finite time convergence to equilibriumis achieved for both the controllers and observer designs. Numericalsimulations validate our design in two different traffic scenarios.

Output Feedback Control of Two-lane Traffic Congestion