Performance-Barrier-Based Event-Triggered Boundary Control of Congested ARZ Traffic PDEs

Abstract

Employing the recent concept of performance-barrier-based event-triggered control (P-ETC), this study presents an event-triggered PDE backstepping design for stabilizing stop-and-go oscillations in Traffic flow by actuating a variable speed limit (VSL) located at the downstream boundary of a freeway segment. The system is described by the linearized Aw-Rascle-Zhang (ARZ) macroscopic Traffic model, a 2 × 2 coupled hyperbolic system. Compared to continuous-time control, event-triggered control (ETC) generates piecewise-constant variable speed limit (VSL) commands, which are more likely to be adhered to by human drivers. Unlike the existing regular ETC (R-ETC) approach that conservatively enforces strict decreases in the closed-loop system Lyapunov function, our proposed P-ETC approach allows for increases as long as the Lyapunov function remains below an acceptable performance barrier. This flexibility results in fewer control updates of P-ETC compared with R-ETC while ensuring Zeno-free behavior and exponential convergence to zero in the spatial L2 norm. Comparative simulation results illustrate the benefits of the performance-barrier design in terms of safety, driver comfort, travel time, fuel consumption. The proposed P-ETC reduces discomfort nearly in half relative to driver behavior without VSL, while increasing the driver safety by as much as 10×, measured by the average dwell time, relative to the R-ETC VSL schedule.