Scheduling for finite time consensus

Ko, Chih-Kai; Shi, Ling

doi:10.1109/acc.2009.5160026

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…We call the above method of implementing Algorithm 1 and consensus protocol (10) simultaneously as ADMM live. Now, we compare the performance of ADMM live with the Metropolis weights using the following example.…”

Section: B New Agents Enter a Network: Admm Live -A Variation Of Algo...mentioning

confidence: 99%

“…In all consensus protocols, an important parameter is the time required to reach average consensus. One line of literature focuses on algorithms which achieve consensus in finite time [8]- [10]. The other line of literature looks at algorithms which achieve consensus asymptotically, while trying to improve the rate of this asymptotic convergence [6], [11].…”

Section: Introductionmentioning

confidence: 99%

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Distributed computation of fast consensus weights using ADMM

Rokade¹,

Kalaimani²

2020

Preprint

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We consider the problem of achieving average consensus among multiple agents, where the inter-agent communication network is depicted by a graph. We consider the discrete-time consensus protocol where each agent updates its value as a weighted average of its own value and those of its neighbours. Given a graph, it is known that there exists a set of 'optimal weights' such that the agents reach average consensus asymptotically with an optimal rate of convergence. However, existing methods require the knowledge of the entire graph to compute these optimal weights. We propose a method for each agent to compute its set of optimal weights locally, i.e., each agent only has to know who are its neighbours. The method is derived by solving a matrix norm minimization problem subject to linear constraints in a distributed manner using the Alternating Direction Method of Multipliers (ADMM). We illustrate our results using numerical examples and compare our method with an existing method called the Metropolis weights, which are also computed locally.

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Section: B New Agents Enter a Network: Admm Live -A Variation Of Algo...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed computation of fast consensus weights using ADMM

Rokade¹,

Kalaimani²

2020

Preprint

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“…Our work is most closely related to [17] where Ko and Shi examined link scheduling on the complete graph to achieve finite-time average-consensus. They provided necessary and sufficient conditions for finite-time consensus and computed the minimum consensus time on the boolean hypercube.…”

Section: Related Workmentioning

confidence: 99%

“…Boyd et al [13] studies the ǫ-average time of (2) when the W (t)'s are drawn independently and uniformly at random from S ′ 1 ∩G. In terms of finite-time consensus, [17] showed that …”

Section: G-admissible Factorizationmentioning

confidence: 99%

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On matrix factorization and finite-time average-consensus

Gao

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-We study the finite-time average-consensus problem for arbitrary connected networks. Viewing this consensus problem as a factorization of 1 n 11T by suitable families of matrices, we prove the existence of a finite factorization and provide tight bounds on the size of the minimal factorization by exhibiting finite-time average-consensus algorithms and bounding their runtimes. We also show that basic matrix theory yields insights into the structure of finite-time consensus algorithms.

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Speeding up finite-time consensus via minimal polynomial of a weighted graph — A numerical approach

Wang

Ong

2018

Automatica

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Reaching consensus among states of a multi-agent system is a key requirement for many distributed control/optimization problems. Such a consensus is often achieved using the standard Laplacian matrix (for continuous system) or Perron matrix (for discrete-time system). Recent interest in speeding up consensus sees the development of finite-time consensus algorithms.This work proposes an approach to speed up finite-time consensus algorithm using the weights of a weighted Laplacian matrix.The approach is an iterative procedure that finds a low-order minimal polynomial that is consistent with the topology of the underlying graph. In general, the lowest-order minimal polynomial achievable for a network system is an open research problem.This work proposes a numerical approach that searches for the lowest order minimal polynomial via a rank minimization problem using a two-step approach: the first being an optimization problem involving the nuclear norm and the second a correction step. Several examples are provided to illustrate the effectiveness of the approach.

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Scheduling for finite time consensus

Cited by 6 publications

References 22 publications

Distributed computation of fast consensus weights using ADMM

Distributed computation of fast consensus weights using ADMM

On matrix factorization and finite-time average-consensus

Speeding up finite-time consensus via minimal polynomial of a weighted graph — A numerical approach

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