Distributed Event-Triggered Formation Control of Multiagent Systems via Complex-Valued Laplacian

Event-triggered formation control of multiagent systems under an undirected communication graph is investigated using complex-valued Laplacian. Both continuous-time and discrete-time models are considered. The dynamics of each agent is described by complex-valued differential or difference equations. For each agent, only the discrete-time information of its neighbors is used in the design of formation controllers and event triggers. Triggering time instants for any agent are determined by certain events that depend on the states of its neighboring agents. Continuous updating of controllers and continuous communication among neighboring agents are avoided. The obtained results show that formation can reach specific but arbitrary formation shape. Furthermore, it is shown that the closed-loop system does not exhibit the Zeno phenomenon for the continuous-time dynamics case or the Zeno-like behavior for the discrete-time dynamics case. Finally, numerical simulations for both the continuous-time and the discrete-time dynamics cases are presented to illustrate the effectiveness of the proposed distributed event-triggered control methods.