Online set-point estimation for feedback-based traffic control applications

This paper deals with traffic control at motorway bottlenecks assuming the existence of an unknown, time-varying, Fundamental Diagram (FD). The FD may change over time due to different traffic compositions, e.g., light and heavy vehicles, as well as in the presence of connected and automated vehicles equipped with different technologies at varying penetration rates, leading to inconstant and uncertain driving characteristics. A novel methodology, based on Model Reference Adaptive Control, is proposed to robustly estimate in real-time the time-varying set-points that maximise the bottleneck throughput, particularly useful when the traffic is regulated via a feedback-based controller. Furthermore, we demonstrate the global asymptotic stability of the proposed controller through a Lyapunov analysis. The effectiveness of the proposed approach is evaluated via simulation experiments, where the estimator is integrated into a feedback ramp-metering control strategy, employing a second-order multi-lane macroscopic traffic flow model, modified to account for time-varying FDs.