Randomized Matrix Weighted Consensus

Abstract

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.

arXiv comment32 pages, 6 figures, preprint

References in corpus (6)

• Theory and Applications of Matrix-Weighted Consensus
• Discrete-Time Matrix-Weighted Consensus
• Cooperative opinion dynamics on multiple interdependent topics: Modeling and analysis
• Location-Aided Fast Distributed Consensus in Wireless Networks
• Randomized Matrix Weighted Consensus
• Bearing-Based Network Localization Under Randomized Gossip Protocol

Cited by in corpus (2)

• Randomized Matrix Weighted Consensus
• Bearing-Based Network Localization Under Randomized Gossip Protocol