Event-Triggered Scheme on Appointed-Time Leader-Following Consensus of Multi-Agent Systems with Prescribed Performance

The appointed-time leader-following consensus (ALFC) problem for second-order multi-agent systems (MASs) with prescribed performance (PP) under directed graphs by means of an event-triggered control (ETC) scheme is investigated in this paper. Based on Lyapunov theory, we prove that the position tracking error reaches an arbitrarily small specified compact set in appointed-time. Besides, the proposed distributed protocol guarantees the PP of the controlled system, which means that the cumulative position difference (CPD) stays within a preset region being determined by a novel performance function. In addition, the proposed event-triggered mechanism sufficiently reduces the frequency of control's update and no Zeno behavior in the MASs. Theoretical results are supported by simulations.