Randomized Matrix Weighted Consensus
Nhat-Minh Le-Phan, Minh Hoang Trinh, Phuoc Doan Nguyen
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 an 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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><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.