Event-triggered Varying Speed Limit Control of Stop-and-go Traffic

Abstract This paper develops event-triggered boundary control strategies for varying speed limit (VSL) located at a freeway segment. The stop-and-go traffic oscillations are suppressed by regulating the velocity of vehicles that leave the segment. The controlled velocity signal is only updated when a event triggering condition is satisfied. Compared with the continuous input signal, the event-based controller presents as a more realistic setting to implement by VSL on a digital platform which allows the adaptation time for drivers to follow the advisory speed. The traffic dynamics of density and velocity are described with linearized Aw-Rascle-Zhang (ARZ) macroscopic traffic partial differential equation (PDE) model which results in a 2 × 2 coupled hyperbolic system. The event-triggered boundary controllers rely on the emulation of the full state backstepping boundary feedback and two different Lyapunov-based event-triggered strategies to determine the time instants at which the control value must be sampled/updated. One of the event-triggered strategies makes use of a dynamic triggering condition under which it is possible to state the existence of a uniform minimal dwell-time (independent of initial conditions). The exponential stability under event-triggered control is achieved and validated with numerical simulations.