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.