Date(s) - 5 Dec 2018
1:10 PM - 2:00 PM
2222 Coover Hall
Speaker: Seyyed Shaho Alaviani, ECpE Graduate Student
Adviser: Nicola Elia
Title: A Distributed Algorithm for Solving Linear Algebraic Equations Over Random Networks
Abstract: In this paper, the problem of solving linear algebraic equations of the form Ax=b among multi agents is considered. It is assumed that the interconnection graphs over which the agents communicate are random. It is assumed that each agent only knows a subset of rows of the partitioned matrix [A,b]. The problem is formulated such that this formulation does not require distribution dependency of random communication graphs. The random Krasnoselskii-Mann iterative algorithm is applied for almost sure convergence to a solution of the problem for any matrices A and b and any initial conditions of agents’ states. The algorithm converges almost surely independently from the distribution and, therefore, is amenable to completely asynchronous operations without B-connectivity assumption. Based on initial conditions of agents’ states, we show that the limit point of the sequence generated by the algorithm is determined by the unique solution of a convex optimization problem independent from the distribution of random communication graphs. This paper has been accepted at IEEE Conference on Decision and Control, December 17-19, Miami Beach, FL, USA, 2018.