Stabilizing piecewise linear state feedback controllers for freeway networks

This paper considers a freeway traffic system regulated via ramp metering. By adopting the Asymmetric Cell Transmission Model, a freeway stretch can be seen as a discrete-time piecewise affine system. A general state-space representation for this system is reported in the paper, for a generic number of cells composing the freeway stretch and a generic number of on-ramps. Piecewise linear full-state feedback controllers are defined for each on-ramp, for which the stabilizing properties are investigated. In particular the regulator gains are determined to guarantee the stability of the controlled system with reference to the error signal. The results reported in the paper suggest that, instead of full-state regulators, local regulators can be employed, relying on the state measurements of a subset of cells that are in the neighborhood of the on-ramp.