Output-Feedback Model Predictive Control for Ramp Metering

We study the stability of traffic flow under output-feedback ramp metering in cases of incomplete information about the traffic flow state. We propose a set-membership estimation method for the cell transmission model with capacity drops and design a model predictive controller accordingly. This controller has linear running and terminal costs in cell densities, and its output comprises density measurements from a subset of the cells, e.g., through loop detectors or connected vehicles. For a line network, we provide sufficient conditions under which the traffic system is input-to-state stable, meaning the ramp queue length remains bounded, on the control horizons, cost coefficients, and the inflows at the ramps. In addition to the proposed controller, we provide extensive simulations of other ramp metering algorithms in the literature as baselines for evaluating performance. Simulation results show that traffic flow is unstable without ramp metering or with other ramp metering methods under high inflows, congested initial conditions, and incomplete state measurements. In contrast, the designed controller stabilizes traffic flow and provides higher throughput with measurements from an arbitrary subset of the cells.