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. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)