2018/09/21 by S. Sh. Alaviani, Alaviani, S. Sh., N. Elia +1
Computer Science · Mathematics · Physics and Astronomy · #Distributed Control Multi-Agent Systems #FOS: Electrical engineering #Opinion Dynamics and Social Influence #Random Matrices and Applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1809.07955
openalex publication_date 2018/09/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this paper, we consider the problem of solving linear algebraic equations of the form Ax=b among multi agents which seek a solution by using local information in presence of random communication topologies. The equation is solved by m agents where each agent only knows a subset of rows of the partitioned matrix [A,b]. We formulate the problem such that this formulation does not need the distribution of random interconnection graphs. Therefore, this framework includes asynchronous updates or unreliable communication protocols without B-connectivity assumption. We apply the random Krasnoselskii-Mann iterative algorithm which converges almost surely and in mean square to a solution of the problem for any matrices A and b and any initial conditions of agents' states. We demonestrate that the limit point to which the agents' states converge is determined by the unique solution of a convex optimization problem regardless of the distribution of random communication graphs. Eventually, we show by two numerical examples that the rate of convergence of the algorithm cannot be guaranteed.