Event-triggered PDE-based control of freeway traffic flow with connected/automated vehicles

Abstract This paper addresses the event-triggered control problem for a modified Aw–Rascle–Zhang (ARZ) traffic model under congestion conditions. The considered ARZ-type model, described by non-linear first-order hyperbolic partial differential equations, represents traffic flow involving both adaptive cruise control-equipped (ACC-equipped) vehicles and human-driven vehicles. The control inputs are time-gap settings for ACC-equipped vehicles that are updated based on a suitable event-triggering condition. For the linearized and transformed system (a 2 $\times $ 2 linear hyperbolic system with in-domain control and dynamic boundary condition), we provide input-to-state stability estimates (in the sup-norm) with respect to actuation errors. Based on a small-gain approach, we design an appropriate triggering rule (yielding small-gain-based event triggering condition). We ensure the exponential stability in the sup-norm of the closed-loop system and Zeno-free behaviour. Numerical simulations illustrate the efficiency of the proposed control strategy in stabilizing traffic flow.