Dynamic event-triggered strategies for tracking control of directed multi-agent systems with Lipschitz nonlinear dynamics

This article considers synchronization of Lipschitz nonlinear multi-agent systems under dynamic event-triggered mechanisms in a directed network. To achieve synchronization with less requirement of communications, a distributed event-triggered state feedback control protocol as well as corresponding dynamic event-triggered mechanism are proposed in a directed network, where the designed dynamic event-triggered mechanism can boil down to existing static triggering mechanisms as special examples. Then, our scheme is extended to design an observer-based event-triggered protocol and a dynamic triggering law when the system states are unmeasurable. It is shown that the proposed dynamic event-triggered mechanisms can not only guarantee synchronization of Lipschitz nonlinear multi-agent systems with Zeno-freeness, but also avoid continuous communications among agents. Moreover, by comparing the static and dynamic trigger mechanisms, it proves that the minimum inter-execution time of the dynamic trigger mechanism cannot be smaller than that of the static case. Finally, two numerical examples are given to verify the theoretical analysis.