Simultaneous Stabilization of Traffic Flow on Two Connected Roads

TL;DR

This paper develops a boundary state feedback control law to stabilize traffic flow on two connected roads governed by nonlinear PDEs, using ramp metering at the junction, validated through numerical simulations.

Contribution

It introduces a novel control law for stabilizing interconnected second-order traffic models at a junction, addressing under-actuated boundary control challenges.

Findings

Achieved exponential stability of traffic flow to a steady state.

Validated control effectiveness through numerical simulations.

Demonstrated stabilization for various equilibrium conditions.

Abstract

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.