Optimal observer‐based output feedback controller for traffic congestion with bottleneck

Abstract

AbstractThis article designs an optimal observer‐based output feedback control for traffic breakdown to dissolve traffic congestion using the backstepping method and optimization. The linearized Aw–Rascle–Zhang model is used to represent the congested traffic dynamics resulting from traffic breakdown. Based on the factors leading to traffic breakdown, we take into account the boundary conditions consisting of a boundary with a constant density and a speed drop at the upstream inlet of a bottleneck, and a boundary with a disturbance of inflow (high traffic demand) at the inlet of the road segment under consideration. To dissolve traffic congestion, a dynamic feedback controller is designed at the upstream boundary. By using the backstepping approach, an observer‐based output feedback controller is computed to guarantee the integral input‐to‐state stability of the closed‐loop system. By establishing an optimization problem and solving it, the optimal value of the considered class controller is obtained. The performance of the output feedback controller is also validated by numerical simulations.