A framework for decentralised feedback connectivity control with application to sensor networks

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In this article, we propose a decentralised algorithm for connectivity maintenance in a distributed sensor network. Our algorithm uses the dynamics of a consensus algorithm to estimate the connectivity of a network topology in a decentralised manner. These estimates are then used to inform a decentralised control algorithm that regulates the network connectivity to some desired level. Under certain realistic assumptions we show that the closed-loop dynamics can be described as a consensus algorithm with an input, and eventually reduces to a scalar system. Bounds are given to ensure the stability of the algorithm and examples are given to illustrate the efficacy of the proposed algorithm. 1. Introduction Recent years have witnessed a growing interest in the control community in problems that arise when dynamic systems evolve over graphs. While the most high profile of these applications are in consensus applications such as formation flying and synchronisa-and Mehra 2007), many other applications have arisen where the manner in which the network topologies change affects the performance of algorithms over which they evolve. In such applications , an essential requirement is that the topology of the graph be such that some basic properties required to support communication and control are satisfied, the most basic of these being that the network be connected. Considerations of this kind have given rise to the emerging field of network topology control. Roughly speaking, a graph is (strongly) connected if there exists at least one communication path from any one network node to another. Clearly, graph connectivity is an essential component in situations where a group of network nodes must work together, in a decentralised manner, to achieve some global task. This issue of graph connectivity is therefore very important and …