Effects of changing the weights of arcs on the consensus convergence rate of a leader–follower multi-agent system
Shanshan Gao,
Shenggui Zhang and
Xinzhuang Chen
Chaos, Solitons & Fractals, 2023, vol. 172, issue C
Abstract:
For a first-order leader–follower multi-agent system (MAS), its consensus convergence rate is determined by the algebraic connectivity (the smallest real part of nonzero eigenvalues) of the corresponding directed graph of its interaction topology. In this paper, effects of changing the weights of arcs among the followers on the algebraic connectivity are investigated for a leader–follower topology with a weighted strongly connected directed graph as the followers’ interaction topology. If the weight of one arc decreases (increases), the algebraic connectivity increases (decreases) if and only if the entry of the Fiedler vector corresponding to its head is smaller than that of its tail. For arcs with a common head, the arc whose tail corresponds to the largest (smallest) entry of the Fiedler vector improves the algebraic connectivity most if the weight of one of these arcs decreases (increases). A necessary and sufficient condition for improving the algebraic connectivity is also proposed for decreasing (increasing) the weights of multiple arcs by the entries of the Fiedler vector corresponding to the vertices of the arcs and the amounts of the weight changes. Moreover, a method of choosing an optimal set of arcs that improve the algebraic connectivity most is proposed if the changing weights are given. Finally, several numerical experiments are given to illustrate the theoretical results.
Keywords: Leader–follower MAS; Algebraic connectivity; Fiedler vector; Strongly connected weighted directed graph; Consensus convergence rate (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077923004915
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004915
DOI: 10.1016/j.chaos.2023.113590
Access Statistics for this article
Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros
More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().