Analysis of the Godunov-Based Hybrid Model for Ramp Metering and Robust Feedback Control Design

This paper presents the detailed analysis of a Godunov-approximation-based dynamics model for an isolated traffic ramp metering problem. The model for the system is based on a Godunov numerical scheme so that the lumped parameter approximation retains the weak solution shock and rarefaction wave properties exhibited by the distributed model. This paper explicitly considers uncertainty in the system parameters and shows how to design controllers that are robust to those uncertainties. Simulations are performed to show the effectiveness of the proposed control law.