Output-Feedback PDE Control of Traffic Flow on Cascaded Freeway Segments

Abstract

We develop in this paper a boundary output feedback control law for an underactuated network of traffic flow on two connected roads; 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) of traffic density and velocity. The control objective is to stabilize the traffic network system on both roads around a chosen reference system. Using a ramp metering located at the outlet of the outgoing road, we actuate the traffic flux leaving this considered domain. Boundary measurements of traffic flux and velocity are taken at the junction connecting the two road segments. A delay-robust full state feedback control law and a boundary observer are designed for this under-actuated network of two systems interconnected through their boundaries. Each system consists of two hetero-directional linear first-order hyperbolic PDEs. The exponential convergence to the reference system is achieved.