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Abstract 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.