Feedback Coordinated Ramp Control using Distributed Modeling and Godunov Based Optimal Allocation

This paper presents a feedback control design for a coordinated ramp metering problem. We design an optimal traffic allocation scheme for ramps based on Godunov’s numerical method and using distributed-diffusive model. Most of the previous work for designing feedback control for ramp metering is based on either the discretized linear methods such as ALINEA or nonlinear methods based on the traffic ODEs. Limitation with these models is that neither do they produce vanishing viscosity weak solutions in the limit nor do they satisfy the entropy conditions. We utilize distributive-diffusive model to construct a condition for maximizing the traffic flow on the freeway stretch. And then design a Godunov method based optimal allocation scheme which gives us the actual control for each ramp individually. We show the stability properties of the closed-loop system and validate the effectiveness of the feedback control law by running a simulation using real traffic flow measurements with parameter estimation.