Stop-and-go suppression in two-class congested traffic

Abstract

This paper develops an output feedback control law in order to damp out traffic oscillations in the congested regime of the linearized two-class Aw-Rascle (AR) traffic model. The macroscopic second-order two-class AR traffic model consists of four hyperbolic partial differential equations (PDEs) describing the dynamics of densities and velocities on freeway. Each vehicle class is characterized by its own vehicle size and driver’s behavior. The considered equilibrium profiles of the model represent evenly distributed traffic with constant densities and velocities of both classes along the investigated track section. After linearizing the model equations around those equilibrium profiles, it is observed that in the congested traffic one of the four characteristic speeds is negative, whereas the remaining three are positive. Backstepping control design is employed to stabilize the 4 × 4 heterodirectional hyperbolic PDEs. The control input actuates the traffic flow at outlet of the investigated track section and is realized by a ramp metering. The output feedback controller is obtained by designing an anti-collocated observer and combining it with a full state feedback result. Overall, the output feedback control law achieves the damping of stop-and-go waves in finite time by measuring the velocities and densities of both vehicle classes at the inlet of the investigated track section. The performance of the developed controller is verified by simulation of the linearized model and quantified by performance indices for the fuel consumption, comfort and total travel time.