Necessary and Sufficient Conditions for Solving Leader-Following Problem of Multi-Agent Systems with Communication Noises

摘要

The leader-following problem of first-order integral multi-agent systems with communication noises is investigated in this paper.To attenuate the noise's effect,a positive time-varying gain α(t) is employed in the protocol.It is proved that the proposed protocol can solve the mean square leader-following problem if the following conditions hold: 1) the communication topology graph has a spanning tree;2)∫0∞ α(t)dt=∞;3) limt→∞α(t)=0.The requirements on α(t) are different from most existing papers,where α(t) is required to satisfy that ∫0∞α2(t)dt =∞and ∫0∞α2(t)dt < ∞.It turns out that ∫0∞α2(t)dt < ∞implies limt→∞α(t) = 0,if α(t) is uniformly continuous.Therefore this paper relaxes the requirements on α(t) to some extent.In addition,under the mild condition (α(t) is uniformly continuous) these three conditions are necessary as well.Furthermore,if ∫0∞ α2(t)dt < ∞,the employed protocol is proved to be able to solve the almost sure leader-following problem of first-order integral multi-agent system.Finally,a simulation example is provided to verify the effectiveness of the employed protocols.