Analysis of the urban network gating problem: An SOS programming approach

The paper presents a Sum-of-Squares programming-based method for the analysis of the nonlinear urban network gating problem. The goal of the analysis is the determination of the maximum control input by which the stability of the system is guaranteed and traffic congestion is avoided. The urban traffic dynamics is modeled as a parameter-dependent polynomial system, which depends on the nonlinear and uncertain network fundamental diagram. The formulation of the Sum-of-Squares optimization procedure uses a parameter-dependent polynomial Control Lyapunov Function for the computation of the maximum controlled inflow. The results of the nonlinear analysis can be applied to the analysis of the urban network gating problem and the synthesis of the gating control. The efficiency of the optimization process is demonstrated through case studies.