Consensus of networked hyperbolic systems via event-triggered boundary feedback control

This paper investigates the consensus problem of networked hyperbolic partial differential equation (PDE) systems for reaching an agreement over the whole spatial domain via event-triggered boundary feedback control. Consensus controllers are proposed for each PDE system based on the boundary information of its neighboring systems, where both centralized and distributed event-triggered strategies are designed in order to reduce the controller updating frequency. By employing the Lyapunov technique, sufficient conditions with respect to system matrices, event-triggered conditions and the undirected communication topology are obtained to ensure consensus of the networked systems, and it is proved that the Zeno behavior can also be avoided. Finally, the consensus control of a three-lane freeway traffic flow system modeled by Aw-Rascle-Zhang Equations is given as an application example, and the numerical simulation is carried out to validate the theoretical results.