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

Knorn, Florian; Stanojevic, Rade; Corless, Martin; Shorten, Robert

doi:10.1080/00207179.2010.530866

Cited by 13 publications

(27 citation statements)

References 16 publications

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“…In the context of this paper and the topology control problem discussed in [6], we are interested in the following type of n-dimensional positive systems with an input term:…”

Section: Resultsmentioning

confidence: 99%

“…This also allows us to determine how the control gain η must be chosen so that the closed loop system is stable, which is reported in depth in [6]. Note again, that any other consensus scheme (to which Theorem 2 can be applied) may be used as well.…”

Section: Control Strategymentioning

confidence: 99%

“…In [6] we describe several methods of estimating this important, global quantity in a distributed way. With the algorithms provided therein, each node in a network is able to estimate the second eigenvalue using only local, readily available information.…”

Section: Distributed Averaging and Topology Controlmentioning

confidence: 99%

“…This issue of graph connectivity is therefore very important and has achieved much attention in various contexts recently. In this paper we describe a recently proposed decentralised topology control algorithm [6] and suggest a simple way of adding weights to the states. This algorithm was posed to overcome some common assumptions in topology control (namely, that the underlying graph is symmetric).…”

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confidence: 99%

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A Problem in Positive Systems Stability Arising in Topology Control

et al. 2009

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We present a problem in the stability of switched positive systems that arises in network topology control. Preliminary results are given that guarantee stability of a network topology control problem under certain assumptions. Roughly speaking, these assumptions reduce the underlying stability problem to a nonlinear consensus problem with a driving term, that eventually becomes a Lur'e problem. Simulation results are given to illustrate our algorithm. While these results indicate that our assumptions can be removed, a proof of the general stability problem remains open. IntroductionRecent 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 synchronisation problems, [4,8,11], many other applications have arisen where the manner in which network topologies change affect the performance of algorithms that are run over these networks. In such applications, an essential requirement is that the topology of the graph be such that some properties required to support communication and control are satisfied, the most basic of these being that the network is connected. Considerations of this kind have given rise to the emerging field of network topology control. Clearly, graph connectivity is an essential component in

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“…In the context of this paper and the topology control problem discussed in [6], we are interested in the following type of n-dimensional positive systems with an input term:…”

Section: Resultsmentioning

confidence: 99%

Section: Control Strategymentioning

confidence: 99%

Section: Distributed Averaging and Topology Controlmentioning

confidence: 99%

mentioning

confidence: 99%

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A Problem in Positive Systems Stability Arising in Topology Control

et al. 2009

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“…Furthermore, the Fiedler value is a nondifferentiable function of the Laplacian matrix, which presents difficulties in designing feedback controllers to maintain it positive definite. Ways to overcome this problem involve either positive definiteness constraints on the determinant of the Laplacian matrix that is a differentiable function of the Laplacian [43], or distributed consensus on either Laplacian eigenvectors [44], [45] or on the network structure itself [46] for local estimation of the Fiedler value of the overall network.…”

mentioning

confidence: 99%

Graph-theoretic connectivity control of mobile robot networks

2011

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This paper develops an analysis for groups of vehicles connected by a communication network; control laws are formulated to accomplish tasks requiring rendezvous, and swarm in group formations.By Michael M. Zavlanos, Member IEEE, Magnus B. Egerstedt, Senior Member IEEE, and George J. Pappas, Fellow IEEE ABSTRACT | In this paper, we provide a theoretical framework for controlling graph connectivity in mobile robot networks.We discuss proximity-based communication models composed of disk-based or uniformly-fading-signal-strength communication links. A graph-theoretic definition of connectivity is provided, as well as an equivalent definition based on algebraic graph theory, which employs the adjacency and Laplacian matrices of the graph and their spectral properties. Based on these results, we discuss centralized and distributed algorithms to maintain, increase, and control connectivity in mobile robot networks. The various approaches discussed in this paper range from convex optimization and subgradient-descent algorithms, for the maximization of the algebraic connectivity of the network, to potential fields and hybrid systems that maintain communication links or control the network topology in a least restrictive manner. Common to these approaches is the use of mobility to control the topology of the underlying communication network. We discuss applications of connectivity control to multirobot rendezvous, flocking and formation control, where so far, network connectivity has been considered an assumption.

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Connectivity of Dynamic Graphs

Zavlanos¹,

Pappas²

2014

Encyclopedia of Systems and Control

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Dynamic networks have recently emerged as an efficient way to model various forms of interaction within teams of mobile agents, such as sensing and communication. This article focuses on the use of graphs as models of wireless communications. In this context, graphs have been used widely in the study of robotic and sensor networks and have provided an invaluable modeling framework to address a number of coordinated tasks ranging from exploration, surveillance, and reconnaissance to cooperative construction and manipulation. In fact, the success of these stories has almost always relied on efficient information exchange and coordination between the members of the team, as seen, e.g., in the case of distributed state agreement where multi-hop communication has been proven necessary for convergence and performance guarantees.

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

Cited by 13 publications

References 16 publications

A Problem in Positive Systems Stability Arising in Topology Control

A Problem in Positive Systems Stability Arising in Topology Control

Graph-theoretic connectivity control of mobile robot networks

Connectivity of Dynamic Graphs

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