Stability analysis of controlled freeway traffic systems with different on-ramp configurations

摘要

This paper considers a freeway stretch controlled via ramp metering and proposes a stability analysis for this system. The dynamics of the system is represented with the Asymmetric Cell Transmission Model, so that a freeway stretch can be seen as a piecewise-affine system switching among different sets of linear difference equations. The stability analysis is firstly referred to the uncontrolled system and, secondly, to the closed-loop system in which a switching proportional feedback control law is applied. In particular, different on-ramp configurations are analysed, including to the two extreme cases of only one on-ramp in a freeway stretch or on-ramps in each cell of the freeway stretch.