Stability of Local On‐Ramp Metering Control Laws

A framework for stability analysis of local on‐ramp metering control strategies based on the cell transmission model is presented. Within this framework, it is possible to formulate Lyapunov and input‐state stability results for on‐ramp metering control strategies in an open section of highway with on‐ramps. Using this analysis, recommendations for the design of on‐ramp metering control laws set points are derived. Two examples on the use of such analysis are presented. One deals with the stability analysis of a local on‐ramp metering control law and the other with the design of a disturbance observer that, used in combination with the local on‐ramp metering control law, provides a more robust response to traffic regulation. Simulation results are included that confirm the possibility of using this framework to test the impact of local on‐ramp metering control strategies.