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Ramp metering, which regulates the flow entering the freeway, is one of themost effective freeway traffic control methods. This paper introduces anoutput-feedback adaptive approach to ramp metering that combines modelpredictive control (MPC) with set-membership parameter and state estimation.The set-membership estimator is based on a mixed-monotone embedding ofunderlying traffic dynamics. The embedding is also used as the modeling basisfor MPC optimization. For a freeway stretch with unknown parameters and partialmeasurement on the freeway mainline, we provide sufficient conditions on thecontrol horizon, cost functions, terminal sets of MPC, and inflow demand at theramps such that the queue lengths in the closed-loop system remain bounded. Thesufficient condition on the demand matches the necessary condition, therebyproving maximal throughput under the proposed controller. The result isstrengthened to input-to-state stability when model parameters and demand areknown. The stability analysis is conducted for the case of constant demand andunbounded on-ramps. The closed-loop trajectory data generated by the proposedcontroller is shown to facilitate finite time estimation of free-flow modelparameters, i.e., free-flow speed and turning ratios. Simulation resultsillustrate stability of the closed-loop system under the proposed controllerwith time-varying demand and few mainline measurements, for which the systembecomes unstable under a well-known approach from the literature. Thisindicates that the proposed controller renders higher throughput than thewell-known approach, possibly using more computing resources.

Output-feedback adaptive model predictive control for ramp metering: a set-membership approach