Robustness of noisy consensus dynamics with directed communication

Young, George Forrest; Scardovi, Luca; Leonard, Naomi Ehrich

doi:10.1109/acc.2010.5531506

Cited by 164 publications

(215 citation statements)

References 24 publications

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“…Combining equations (4), (6), and (7), a distributed estimate of λ 2 can be obtained by solving the equations:…”

Section: A Algebraic Connectivity λmentioning

confidence: 99%

“…The SDE for making a distributed estimate of the total effective graph resistance can be formulated using the result that the linear consensus system with additive white noise of intensisty σ has expected variance at long time, proportional to the total effective graph resistance [6]. As such we introduce the SDE [26]:…”

Section: Total Effective Graph Resistancementioning

confidence: 99%

“…For continuous time linear consensus with time delays, the largest eigenvalue λ n becomes important for guaranteeing convergence [1]. The robustness of a linear consensus system to additive white noise can be quantified using the Total Effective Graph Resistance [6], [7]:…”

Section: Introductionmentioning

confidence: 99%

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Distributed adaptive optimization and control of network structures

Kempton

Herrmann

Bernardo

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Distributed Adaptive Optimization and Control of Network StructuresLouis Kempton, Guido Herrmann and Mario di Bernardo Abstract-In this paper we present a generic distributed weight adaptation framework to optimize some network observables of interest. We focus on the algebraic connectivity λ2, the spectral radius λn, the synchronizability λn/λ2, or the total effective graph resistance Ω of undirected weighted networks, and describe distributed systems for the estimation of these functions and their derivatives for on-line adaptation of the edge weights.

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“…Combining equations (4), (6), and (7), a distributed estimate of λ 2 can be obtained by solving the equations:…”

Section: A Algebraic Connectivity λmentioning

confidence: 99%

Section: Total Effective Graph Resistancementioning

confidence: 99%

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Distributed adaptive optimization and control of network structures

Kempton

Herrmann

Bernardo

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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“…The majorization of a stress function is used in [3] to develop a distributed coordination algorithm that stabilizes the shape of a relative sensing network to a desired formation; robustness of the algorithm against measurement errors in the relative information of neighboring agents is established. Robustness of consensus to noise for directed communication characterized by the H 2 norm of the system is studied in [15]. A stochastic adaptive algorithm approach is used in [4], [5], in which a stochastic approximation type algorithm with a decreasing step size is proposed and convergence results are established with measurement noise.…”

Section: Introductionmentioning

confidence: 99%

Synchronization on the N-torus with noisy measurements

Mahmoudian

Paley

2011

Proceedings of the 2011 American Control Conference

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Abstract-We consider the problem of cooperative control of unmanned vehicles in an uncertain environment in which each vehicle can obtain only noisy measurements of the other vehicles. In particular, we want to establish convergence to a desired formation using a stochastic algorithm with measurement errors. In this paper, the problem of stabilization of parallel formations in a self-propelled particle model is considered, which can be modeled as synchronization on the N -torus in the presence of noisy measurements of relative phase. Simulations are included to illustrate the result.

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“…This is due to the marginally stable nature of the classical consensus algorithms. See also [12] for the trade off between convergence speed and robustness to additive noise of consensus algorithms. To eliminate this random walk behavior, [13] has proposed an algorithm that uses the diminishing step size, see also [14].…”

Section: Introductionmentioning

confidence: 99%

Dynamic average consensus over random networks with additive noise

Wang

Elia

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-In this paper, we consider distributed dynamic average consensus problem in the presence of uncertainties on information exchange. Two categories of noise are used to characterize these uncertainties: the first is multiplicative noise that captures the randomness of network connections, while the second is additive noise that describes several uncertainty sources. We propose an iterative algorithm that allows each agent to compute/track the average of their private dynamic signals in the presence of both kinds of noise. This algorithm relaxes restrictive assumptions on consensus over random directed network topologies, such as doubly stochastic weights, symmetric link switching styles, etc, and introduces new mechanisms for mitigating effects of communication uncertainties on information aggregation.

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Robustness of noisy consensus dynamics with directed communication

Cited by 164 publications

References 24 publications

Distributed adaptive optimization and control of network structures

Distributed adaptive optimization and control of network structures

Synchronization on the N-torus with noisy measurements

Dynamic average consensus over random networks with additive noise

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