Fully distributed bipartite time-varying formation control for uncertain linear multi-agent systems under event-triggered mechanism

This paper addresses the distributed bipartite time-varying formation control for uncertain linear multi-agent systems under limited communication resources. First, the distributed static bipartite control protocol with sampled data is proposed to address the time-varying formation issue. It is noteworthy that in both controller updating and triggering condition monitoring, the communication is only occurred at sampling instants, which saves communication resources and reduces communication burden effectively. Moreover, the nonlinear term in static controller is used to suppress the effect of system uncertainty. Then the fully distributed adaptive bipartite event-triggered control protocol is put forward such that the time-varying formation control can be achieved. Different from the existing results on formation control, the proposed adaptive controller has the following four highlights: (1) it is fully distributed since the global information of network topology and the upper bound of uncertainty are not required; (2) the communication between neighbor agents is conducted at intermittent triggering instants, not real-time, which reduces the communication bandwidth significantly; (3) the communication between neighbors can not only be cooperative, but also be antagonistic, which is more realistic; and (4) the effect of system uncertainty can be suppressed. Furthermore, it is proven that there is no Zeno behavior in both triggering mechanisms. Finally, some numerical examples are presented to demonstrate the feasibility of the main theoretical findings.