Fixed-Time Boundary Stabilization for Aw-Rascle-Zhang Traffic model

Unlike finite-time stability, where the upper bound of the settling time depends on the initial states of the system, the settling time in fixed-time stability is independent of initial states, and thus it can be adjusted in advance. This paper considers the fixed-time boundary stabilization problem of the Aw-Rascle-Zhang (ARZ) traffic model, which is a 2 × 2 coupled hyperbolic system. To stabilize the traffic speed and density to desired steady states in a fixed time, a full state feedback boundary controller is proposed, the practical actuator of which is performed through ramp metering at the downstream boundary. By utilizing spatial transformation and backstepping method, the linearized ARZ model is transformed into a fixed-time stable target system. We employ the characteristics and Lyapunov methods to prove that the linearized ARZ model is fixed-time stable in the sense of L 2 -norm. Furthermore, the upper bound of the settling time is determined solely by the control parameters, and remains independent of initial states. Finally, the numerical simulation is given to validate the theoretical results.