Simultaneous downstream and upstream output-feedback stabilization of cascaded freeway traffic

In this paper, we develop boundary output feedback control laws for traffic flow on two cascaded freeway segments connected by a junction. The macroscopic dynamics are governed the Aw–Rascle–Zhang (ARZ) model in which subsystems of second-order nonlinear partial differential equations (PDEs) describe evolution density and velocity each segment. Due to change road access at junction, different equilibria considered segments. To suppress stop-and-go oscillations roads, consider ramp metering that regulates rate entering from on-ramp mainline freeway. Different designs proposed such stabilization is realized with either located middle junction or outlet only measurements velocity. objective simultaneously stabilize upstream downstream given spatially-uniform constant steady-state. distinct actuation locations motivate our design delay-robust full state laws. based PDE backstepping methodology guarantee exponential stability under-actuated network systems hyperbolic PDEs. Collocated observers construct controllers. Numerical simulations performed validate designs. Stabilization performance compared evaluated Proportional Integral (PI) Robustness delays also investigated.