Exponential Consensus and Flocking in Multi-Agent Systems with Infinite Fading Memory
Abstract
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.
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BibTeX
@misc{pignotti2026exponential,
title = {{Exponential Consensus and Flocking in Multi-Agent Systems with Infinite Fading Memory}},
author = {Cristina Pignotti and Yu-Qing Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02454},
eprint = {2609.02454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02454},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exponential Consensus and Flocking in Multi-Agent Systems with Infinite Fading Memory
AU - Cristina Pignotti
AU - Yu-Qing Wang
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02454
UR - https://arxiv.org/abs/2609.02454
AB - 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.
ER -