Randomized Matrix Weighted Consensus

• Published in: IEEE transactions on network science and engineering Vol. 11; no. 4; pp. 3536 - 3549
• Main Authors: Le-Phan, Nhat-Minh, Trinh, Minh Hoang, Nguyen, Phuoc Doan
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01-07-2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• 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
• ISSN: 2327-4697; 2334-329X
• DOI: 10.1109/TNSE.2024.3376643

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 <inline-formula><tex-math notation="LaTeX">\epsilon</tex-math></inline-formula>-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.