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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

A conjugate gradient framework for finite-time edge consensus in scaled multi-agent networks

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* Corresponding author · click or hover a name for details

pp. 937–956Vol. 29Issue 4April 2026DOI: 10.47974/JIM-2398XML
Received:
01 Apr 2025
Published Online:
06 Apr 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2398
Pages:
937–956

Abstract

The paper investigates the problem of achieving scaled consensus within a finite time in edge dynamics of hybrid multi-agent systems over undirected and directed networks. The main challenge lies in achieving consensus under heterogeneous edge scaling and dynamic topologies. By modeling edge interactions via the line graph and introducing edge scaling through nonzero factors βij ≠ 0, we express the consensus behavior through a linear system representation. A CGM-based distributed algorithm is introduced to solve this system efficiently. According to the theoretical analysis, the algorithm reaches convergence in no more than M steps, with M being the edge count. Simulations confirm rapid convergence and improved accuracy over classical consensus protocols. The innovation lies in leveraging CGM for scalable, edge-based coordination with guaranteed finite-time performance.

Keywords

Subject Classifications

93C1093C2893C8593D4093D50

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