Time-varying formation control with general linear multi-agent systems by distributed event-triggered mechanisms under fixed and switching topologies

This paper investigates the time-varying formation control (TVFC) problem of multi-agent systems (MASs) with general linear dynamics under fixed topology by utilizing event-triggered mechanisms. In order to achieve the TVFC problem, two kinds of distributed event-triggered formation control schemes are proposed. Moreover, the Zeno behavior is excluded under these event-triggered mechanisms. Since these control protocols are constructed on the basis of the sampling information of the event time instants instead of the real-time information of each agent, each agent does not require to communicate continuously with its neighbors, thus effectively reducing the bandwidth requirement of communication and greatly reducing the use of energy in MASs. It deserves to be mentioned that the second control protocol introduces time-varying coupling weights, does not require to utilize any global information of the system networks, and is more suitable for systems with large-scale network. Moreover, the proposed event-triggered formation control protocols are suitable for arbitrarily switching topologies, and its related results are extended to the case of switching topologies. Finally, several examples are introduced to achieve the TVFC problem by utilizing the adaptive event-triggered control protocol, and Zeno behavior is not observed during the process of simulation.