Consensus protocols for networked multi-agent systems with a uniformly continuous quasi-resetting architecture

The consensus problem appears frequently in coordination of multi-agent systems in aerospace science and engineering, and involves the agreement of networked agents upon certain quantities of interest. In this paper, we focus on a new consensus protocol for networked multi-agent systems using a resetting control architecture. Specifically, the control protocol consists of a delayed feedback, quasi-resetting control law such that controller resettings occur when the relative state measurements (i.e., distance) between an agent and its neighbouring agents approach zero. In contrast to standard impulsive resetting controllers, the proposed resetting is uniformly continuous, and hence, our approach does not require any well-posedness assumptions imposed by impulsive resetting controllers. In addition, using a Lyapunov-Krasovskii functional, it is shown that the multi-agent system reaches asymptotic state equipartitioning, where the system steady state is uniformly distributed over the system initial conditions. Finally, we develop transient performance guarantees while accounting for system overshoot and excessive control effort.