Nonlinear Optimal Control of Traffic Flow with Stability Guarantees

Automated vehicles have been proposed as a way to influence traffic flow to avoid congestion and maintain a smooth traffic flow. Experiments have shown that congestion formation can be reproduced in an artificial ring road scenario. We design a model predictive controller for the ring road system assuming heterogeneous drivers and an automated vehicle for which congestion resolution and convergence to a reference speed can be shown. The driver's model captures human driving responses. A stabilizing predictive controller framework is employed under the use of a local controllability assumption connected to a local linear quadratic regulator. A case study shows the efficacy of the proposed controller and provides numerical values for the required prediction horizon, highlighting congestion resolution as well as theoretical conservativeness.