Closed-loop stability of freeway traffic systems with ramp metering control

In this paper, a freeway traffic system regulated with feedback ramp metering controllers is studied. In particular, a switched controller including the proportional-integral feedback regulator PI-ALINEA and a simpler control law is considered. The Asymmetric Cell Transmission Model, properly rewritten as a piecewise-affine system switching among different sets of linear difference equations, is the model adopted for representing the system dynamics. The closed-loop stability of this switched system is investigated in the paper and the obtained results are used to properly calibrate the controller gains. These results are then tested and discussed with a simulation analysis reported in the paper.

I. Introduction

Freeway traffic control has been a relevant research topic for some decades. Among the possible control strategies, one of the most widespread is surely ramp metering, which allows to regulate the traffic flows entering the mainstream by adopting traffic lights at the on-ramps [1]. In order to control traffic with ramp metering, different controllers have been investigated by researchers and in some cases successfully applied in real freeways [2]. One of the first ramp metering controllers is ALINEA, that is a feedback controller of integral type [3], successively extended to become a proportional-integral regulator, called PI-ALINEA. The main aim of these regulators is to track a reference value for the occupancy or for the traffic density.