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 withot 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.
Original language | English (US) |
---|---|
Title of host publication | 2018 IEEE Conference on Decision and Control, CDC 2018 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 83-88 |
Number of pages | 6 |
ISBN (Electronic) | 9781538613955 |
DOIs | |
State | Published - Jul 2 2018 |
Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018 |
Publication series
Name | Proceedings of the IEEE Conference on Decision and Control |
---|---|
Volume | 2018-December |
ISSN (Print) | 0743-1546 |
ISSN (Electronic) | 2576-2370 |
Conference
Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
---|---|
Country/Territory | United States |
City | Miami |
Period | 12/17/18 → 12/19/18 |
Bibliographical note
Funding Information:This work was supported by National Science Foundation under Grant CCF-1320643, Grant CNS-1239319, and AFOSR Grant FA 9550-15-1- 0119..
Funding Information:
This work was supported by National Science Foundation under Grant CCF-1320643, Grant CNS-1239319, and AFOSR Grant FA 9550-15-1-0119.. The work has been done while N. Elia was at Iowa State University. The proofs and extensions of this paper appear in [44].
Publisher Copyright:
© 2018 IEEE.