This paper deals with multi-agent systems that, due to using the generalized proportional Caputo fractional derivative, possess memories. The information exchange between agents does not occur continuously but only at fixed given update times, and the lower limit of the fractional derivative changes according to the update times. Two types of multi-agent systems are studied, namely systems without a leader and systems with a leader. For a generalized proportional Caputo fractional model of multi-agent linear dynamic systems, sufficient conditions for exponential stability via impulsive control are obtained. In the case of the presence of a leader in the multi-agent system, we derive sufficient conditions for the leader-following consensus via impulsive control based on the leader’s influence. Simulation results are provided to verify the essential role of the generalized proportional Caputo fractional derivative and impulsive control in realizing the consensus of multi-agent systems.

本文处理的多智能体系统由于使用广义比例 Caputo 分数导数而具有记忆。代理之间的信息交换不是连续发生的，而是仅在固定的给定更新时间发生，并且分数导数的下限根据更新时间而变化。研究了两种类型的多智能体系统，即没有领导者的系统和有领导者的系统。对于多智能体线性动态系统的广义比例Caputo分数模型，通过脉冲控制获得了指数稳定的充分条件。在多智能体系统中存在领导者的情况下，我们通过基于领导者影响的脉冲控制推导出领导者跟随共识的充分条件。