具有无限衰减记忆的多智能体系统中的指数共识与集群行为

中文摘要 AI 辅助

本文研究由Volterra型无限分布式衰减记忆驱动的多智能体系统的涌现集体动力学。我们建立了统一的理论框架，涵盖一阶观点共识动力学与二阶速度对齐集群运动学。通过引入Dafermos过去历史变换，将控制积分-微分系统重构为扩展乘积希尔伯特空间上的动力学系统。对于一阶动力学，我们证明衰减记忆固有地提供了隐藏的耗散机制，无论是否存在瞬时通信力，均能保证无条件全局指数共识。对于二阶动力学，我们得到纯衰减记忆系统的无条件指数集群行为，并给出同时存在瞬时相互作用时的集群行为充分条件。特别地，当影响函数具有发散尾时，该条件始终满足，即集群行为无条件发生。

英文摘要

In this paper, we study the emergent collective dynamics of multi-agent systems driven by infinite distributed fading memory of Volterra type. We establish a unified theoretical framework covering both first-order opinion consensus dynamics and second-order velocity alignment flocking kinematics. By introducing Dafermos past-history transformations, the governing integro-differential systems are reformulated into dynamical systems on an extended product Hilbert spaces. For first-order dynamics, we prove that fading memory inherently provides a hidden dissipative mechanism, guaranteeing unconditional global exponential consensus with or without instantaneous communication forces. For second-order dynamics, we obtain unconditional exponential flocking for the pure fading memory system and we give a sufficient condition for flocking when an instantaneous interaction is also present. In particular, this condition is always satisfied, namely the flocking occurs unconditionally, when the influence function has a divergent tail.

发表机构

• Università dell’Aquila（阿奎拉大学）
• Dalian University of Technology（大连理工大学）

机构由 AI 辅助整理，请以论文原文为准。