Average Consensus over Mobile Wireless Sensor Networks: Weight Matrix Guaranteeing Convergence without Reconfiguration of Edge Weights.

Martin Kenyeres,Jozef Kenyeres

doi:10.3390/s20133677

Abstract

Efficient data aggregation is crucial for mobile wireless sensor networks, as their resources are significantly constrained. Over recent years, the average consensus algorithm has found a wide application in this technology. In this paper, we present a weight matrix simplifying the average consensus algorithm over mobile wireless sensor networks, thereby prolonging the network lifetime as well as ensuring the proper operation of the algorithm. Our contribution results from the theorem stating how the Laplacian spectrum of an undirected simple finite graph changes in the case of adding an arbitrary edge into this graph. We identify that the mixing parameter of Best Constant weights of a complete finite graph with an arbitrary order ensures the convergence in time-varying topologies without any reconfiguration of the edge weights. The presented theorems and lemmas are verified over evolving graphs with various parameters, whereby it is demonstrated that our approach ensures the convergence of the average consensus algorithm over mobile wireless sensor networks in spite of no edge reconfiguration.

Highlights

From the family of consensus-based algorithms, we focus our attention on average consensus (AC)—a distributed multi-functional algorithm finding the application in various areas
The research presented in this paper is motivated by an effort to simplify AC over Mobile wireless sensor networks (MWSNs) whereby the energy requirements are optimized, and the proper operation of the algorithm is ensured
We propose a weight matrix simplifying AC over MWSNs in communication and computation demands

Summary

Introduction

In many modern multi-agent systems, data aggregation mechanisms are applied to process independently measured data from multiple sources that are often deployed in extensive geographical areas [4,5,6] Their application is indented to ensure sensor measurements with increased confidence, even though the precision of the sensor nodes is affected by many negative environmental factors (e.g., radiation, pressure variations, temperature, etc.) [7,8]. The goal of these mechanisms in multi-agent systems is to calculate/estimate an aggregate function (e.g., the arithmetic mean, the sum, the maximum/the minimum, etc.) from data measured by independent entities in order to create information that cannot be obtained by measurements executed by single sensor nodes, whereby the executed applications are optimized in Sensors 2020, 20, 3677; doi:10.3390/s20133677 www.mdpi.com/journal/sensors

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