Event-triggered boundary consensus for multi-agent systems of hyperbolic balance laws

This study addresses the boundary consensus problem of multi-agent systems, in which each agent is governed by hyperbolic partial differential equations. To reduce the controller update frequency, the event-triggered boundary controller is proposed for each agent based on the boundary state information of its neighbors and itself. Firstly, we present the well-posedness and consensus analysis under undirected communication graphs. By using Lyapunov approach and graph theory, we obtain the sufficient conditions associated with triggering parameters, Laplacian eigenvalues and boundary coefficient matrices for guaranteeing the asymptotic consensus and excluding Zeno behaviors. Next, we further consider the consensus problem under the directed communication topologies, and we also establish the sufficient conditions for ensuring the asymptotic consensus. Finally, we present a three-lane freeway traffic flow system described by Aw–Rascle–Zhang Equations as an example to demonstrate the effectiveness of the designed event-triggered boundary consensus controllers.