Feedback Ramp Metering Using Godunov Method Based Hybrid Model

In this paper, a new feedback control design for an isolated freeway ramp is presented utilizing hybrid dynamics based on Godunov's numerical technique. Previous feedback ramp metering designs have been mainly based on either discretized linearized methods such as ALINEA or nonlinear feedback designs based on ordinary differential equations for the traffic model. These models use lumped parameters, which fail to represent some details of the rarefaction wave phenomenon of the distributed model. Godunov's conditions employ the data known on both sides of each boundary in order to determine the characteristics of the boundary conditions. This paper uses Godunov's hybrid lumped model based on which feedback control design is proposed and simulation results for the model are presented. Real data is collected on one of the major freeway on-ramps in the Las Vegas area. The roadway parameters are estimated using least squares estimator then are used in the proposed Godunov based hybrid model. The proposed feedback ramp control design is compared with the actual ramp control algorithm. Self-tuning adaptive control is also performed using recursive parameter updating with and without exponential forgetting.