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.|
|Number of pages||6|
|State||Published - Jan 18 2019|
|Event||57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States|
Duration: Dec 17 2018 → Dec 19 2018
|Name||Proceedings of the IEEE Conference on Decision and Control|
|Conference||57th IEEE Conference on Decision and Control, CDC 2018|
|Period||12/17/18 → 12/19/18|
Bibliographical noteFunding Information:
This work was supported by National Science Foundation under Grant CCF-1320643, Grant CNS-1239319, and AFOSR Grant FA 9550-15-1- 0119..
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 .