Distributed event-triggered consensus control for multiple Euler–Lagrange systems with transmission delay under directed networks

This article addresses the distributed consensus control for multiple Euler–Lagrange systems under directed networks with time-varying transmission delays. Only some followers can access the information of the leader; communication is directed between agents. A distributed adaptive event-triggered control protocol is designed for the two cases where the generalized velocity of the leader is constant/time varying. When the generalized velocity of the leader is time varying, a distributed adaptive observer is designed to make followers obtain the time-varying information of the leader. Then, Lyapunov stability theory and the Linear matrix inequality algorithm prove the tracking errors can converge to zero in a completely distributed chattering-free manner. With the event-triggered mechanism, the number of communications can be decreased, and the system update frequency and the energy consumption can be reduced effectively. Meanwhile, the elimination of the Zeno behavior is also proved. Finally, the simulation results verify the effectiveness of the two controllers.