Convergence Analysis of Stochastic Consensus over Noisy Networks of Linear Symmetric Agents

Abstract

A multi-agent system over noisy undirected networks with linear symmetric agents is considered. A stochastic consensus algorithm is established and analyzed under the noisy environment. An explicit relation between the number of iterations and the closeness of the agreement is also established. The results are illustrated through a numerical example.

An Averaging Consensus Algorithm and Its Stopping Rule over Noisy Undirected Networks of MIMO Linear Symmetric Agents

“…Note that this result includes the SISO case [4]. In fact, since the noise w ij (k) is a scalar in the SISO case, V becomes a scalar v 2 .…”

“…We give a communication gain to achieve the averaging consensus and the stop-ping rule under an appropriate assumption for the symmetric system. These results include the existing ones [3] and [4] as special cases if the agents are first order systems or SISO symmetric systems.…”

“…This η will be used later. We remark that the MIMO linear symmetric agent includes SISO one investigated in [4] when B and C are vectors and R = 1. It can be also the standard first order agent when A = B = C = R = 1 with η = 1.…”

“…Since communication noise is unavoidable and usually interferes with the information exchange, several stochastic consensus algorithms have been proposed under noisy environment [1,2]. Stopping rules, which provide a relation between the explicit number of iterations and the quality of the consensus, have also been established for stochastic noisy environment, where the agents are assumed to be first order systems [3] or higher order systems [4,5]. The latter employs a linear symmetric system [6].…”

Stochastic Consensus over Time-Varying Networks of Linear Symmetric Agents

“…Finally, we conclude this paper in Section 5. The preliminary versions of this study were presented at conferences [8,9].…”