Model predictive control with state estimation for freeway systems

The objective of the paper is the design of a ramp metering control scheme for freeway systems in which the traffic state estimation is also considered. The development of an approach for estimating the traffic densities is motivated by the fact that traffic flow measurements at some locations are in many cases the only available information obtained by sensors, whereas the knowledge of the traffic density is necessary for determining suitable ramp metering actions. A piecewise-affine version of the Asymmetric Cell Transmission Model is adopted and, on the basis of its operating mode and observability properties, a density estimation mechanism based on switched Luenberger observers is realized. The problem is formulated and solved resorting to Linear Matrix Inequalities. The ramp metering control action is then computed by applying a Model Predictive Control approach that uses state estimates in place of measurements. Some simulation results have been performed to test the effectiveness of the proposed approach.