Lyapunov design of event-based controllers for the rendez-vous of coupled systems
The objective is to present a new type of triggering conditions together with new proof concepts for the event- based coordination of multi-agents. As a ﬁrst step, we focus on the rendez-vous of two identical systems modeled as double integrators with additional damping in the velocity dynamics. The reduced number of agents in the system allows us to illustrate the design of the new triggering rule while avoiding technical issues that arise in the full multi-agent system. We ﬁrst propose an event-triggering policy which relies on a designed clock variable whose dynamics depend on the relative position of the agents. We then explain how to derive self-triggered and time-triggered rules. The overall system is modeled as a hybrid system in each case, and an invariance principle is used to conclude about the rendez-vous. Simulation results are provided to illustrate the efﬁciency of the proposed controllers.