Improving the Performance of a Hierarchical Traffic Flow Control Framework using Lyapunov-based Switched Newton Extremum Seeking

The primary aim of this research paper is to enhance the effectiveness of a two-level infrastructure-based control framework utilized for traffic management in expansive networks. The lower-level controller adjusts vehicle velocities to achieve the desired density determined by the upper-level controller. The upper-level controller employs a novel Lyapunov- based switched Newton extremum-seeking control approach to ascertain the optimal vehicle density in congested cells where downstream bottlenecks are unknown, even in the presence of disturbances in the model. Unlike gradient-based approaches, the Newton algorithm eliminates the need for the unknown Hessian matrix, allowing for user-assignable convergence rates. The Lyapunov-based switched approach also ensures asymptotic convergence to the optimal set point. Simulation results demonstrate that the proposed approach, combining Newton's method with user-assignable convergence rates and a Lyapunov-based switch, outperforms gradient based extremum-seeking in the hierarchical control framework.