Enhancing Traffic Flow in Heterogeneous Freeways: Integration of Multivariable Extremum Seeking and Filtered Feedback Linearization Control

This paper presents a novel control approach for managing traffic flow on heterogeneous freeways, including both human-driven vehicles and autonomous vehicles classes. We introduce an enhanced version of the multi-class METANET model that incorporates state-dependent parameters, enabling a more accurate representation of the macroscopic dynamics of traffic systems. Building on this improved traffic model, we propose a two-level hierarchical control framework to manage traffic flow and reduce congestion effectively. At the upper level, a distributed multi-variable extremum seeking (DMV-ES) control approach determines the optimal densities for different class of vehicles within controlled traffic cells to maximize overall traffic flow while minimizing flow variations between adjacent cells. These densities are then provided as reference inputs to the lower-level controller, where a distributed filtered feedback linearization (D-FFL) control is employed to determine the desired speed commands for the vehicles. The key advantage of the proposed controller is that it requires only limited knowledge of the system, making it well-suited for the uncertain and nonlinear nature of heterogeneous traffic systems. The effectiveness of the proposed scheme is validated through numerical simulations and VISSIM-generated traffic scenarios, demonstrating significant improvements in congestion management and enhanced traffic flow compared to conventional methods.