Adaptive Output Feedback for Aw-Rascle-Zhang Traffic Model in Congested Regime

This paper develops adaptive output feedback control to reduce stop-and-go oscillations in congested traffic regime. The macroscopic traffic dynamics are governed by Aw-Rascle-Zhang(ARZ) model, consisting of second-order, nonlinear hyperbolic PDEs of traffic density and velocity. We linearize the PDE system around steady states of congested traffic regime. The boundary input through ramp metering is then introduced for the linearized ARZ traffic model. The goal is to stabilize the oscillations in a freeway segment upstream of the ramp, without the knowledge of relaxation time and boundary parameter. Control is applied at the outlet and the measurement is taken from the inlet. In the absence of both parameter knowledge and full-state measurement, we use backstepping method to transform the system into an observer canonical form in which unknown parameters multiply with measured output. We obtain a parametric model based on this form and gradient-based parameter estimators are employed. An explicit state observer involving the delayed values of the input and the output is proposed for state estimation. Using the parameter and state estimates, we develop an adaptive output feedback control law, which achieves convergence to the steady states in the $L^{2}$ sense.