Randomized Matrix Weighted Consensus

In this paper, randomized gossip-type matrix weighted consensus algorithms are proposed for both leaderless and leader-follower topologies. First, we introduce the notion of expected matrix weighted network, which captures the multi-dimensional interactions between any two agents in a probabilistic...

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Bibliographic Details
Published in:IEEE transactions on network science and engineering 2024-07, Vol.11 (4), p.3536-3549
Main Authors: Le-Phan, Nhat-Minh, Trinh, Minh Hoang, Nguyen, Phuoc Doan
Format: Article
Language:English
Subjects:
Algorithms
Clocks
Consensus algorithm
formation control
gossip algorithms
Heuristic algorithms
Laplace equations
Location awareness
Matrix weighted consensus
multi-agent systems
network localization
Protocols
randomized algorithms
Topology
Upper bounds
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Summary:In this paper, randomized gossip-type matrix weighted consensus algorithms are proposed for both leaderless and leader-follower topologies. First, we introduce the notion of expected matrix weighted network, which captures the multi-dimensional interactions between any two agents in a probabilistic sense. Under some mild assumptions on the distribution of the expected matrix weights and the upper bound of the updating step size, the proposed asynchronous pairwise update algorithms drive the network to achieve a consensus in expectation. An upper bound of the \epsilon-convergence time of the algorithm is then derived. Furthermore, the proposed algorithms are applied to the bearing-based network localization and formation control problems. The theoretical results are supported by several numerical examples.
ISSN:2327-4697
2334-329X
DOI:10.1109/TNSE.2024.3376643