Decentralised minimum-time average consensus in digraphs

Charalambous, Themistoklis; Yuan, Ye; Yang, Tao; Pan, Wei; Hadjicostis, Christoforos N.; Johansson, Michael A.

doi:10.1109/cdc.2013.6760277

Cited by 13 publications

(12 citation statements)

References 22 publications

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“…The contributions of our paper are the following: 1) First, we enhance a distributed protocol proposed in [17], [18] and used in D-ADMM-FTERC, with a distributed termination mechanism [19], with which each node in a digraph can compute the average consensus over a minimal number of steps and agree with the other nodes in the network when to terminate their iterations, provided they have all computed their exact average. More specifically, we modify the distributed termination mechanism [19] to allow for the nodes to synchronize the optimization steps, without requiring any global information.…”

Section: Our Contributionsmentioning

confidence: 99%

“…In what follows, we present a distributed protocol proposed in [17], [18] with which each node can compute, based on its own local observations and after a minimal number of steps, the exact average. This protocol is based on the algorithm in Proposition 1, with which every node can compute µ j lim t→∞ µ t j in a minimum number of steps.…”

Section: Finite-time Exact Ratio Consensus (Fterc)mentioning

confidence: 99%

“…Next, we provide Theorem 1 from [17], in which it is stated that the exact average µ among the nodes in a strongly connected digraph can be distributively obtained in a finite number of steps.…”

Section: It Has Been Shown Inmentioning

confidence: 99%

“…Theorem 1 ( [17]): Consider a strongly connected graph G(V, E). Let y t j and x t j (for all v j ∈ V and t = 0, 1, 2, .…”

Section: It Has Been Shown Inmentioning

confidence: 99%

See 3 more Smart Citations

Fully Distributed Alternating Direction Method of Multipliers in Digraphs via Finite-Time Termination Mechanisms

Jiang,

Charalambous

2021

Preprint

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In this work, we consider the distributed optimization problem in which each node has its own convex cost function and can communicate directly only with its neighbors, as determined by a directed communication topology (directed graph or digraph). First, we reformulate the optimization problem so that Alternating Direction Method of Multipliers (ADMM) can be utilized. Then, we propose an algorithm, herein called Distributed Alternating Direction Method of Multipliers using Finite-Time Exact Ratio Consensus (D-ADMM-FTERC), to solve the multi-node convex optimization problem, in which every node performs iterative computations and exchanges information with its neighbors. At every iteration of D-ADMM-FTERC, each node solves a local convex optimization problem for the one of the primal variables and utilizes a finite-time exact consensus protocol to obtain the optimal value of the other variable, since the cost function for the second primal variable is not decomposable. Since D-ADMM-FTERC requires to know the upper bound on the number of nodes in the network, we furthermore propose a new algorithm, called Fully D-ADMM Finite-Time Distributed Termination (FD-ADMM-FTDT) algorithm, which does not need any global information. If the individual cost functions are convex and not-necessarily differentiable, the proposed algorithms converge at a rate of O(1/k), where k is the iteration counter. Additionally, if the global objective function is strongly convex and smooth, the proposed algorithms have an "approximate" R-linear convergence rate. The efficacy of FD-ADMM-FTDT is demonstrated via a distributed l1 regularized logistic regression optimization example. Additionally, comparisons with other state-of-the-art algorithms are provided on largescale networks showing the superior precision and time-efficient performance of FD-ADMM-FTDT.

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Section: Our Contributionsmentioning

confidence: 99%

Section: Finite-time Exact Ratio Consensus (Fterc)mentioning

confidence: 99%

Section: It Has Been Shown Inmentioning

confidence: 99%

“…Theorem 1 ( [17]): Consider a strongly connected graph G(V, E). Let y t j and x t j (for all v j ∈ V and t = 0, 1, 2, .…”

Section: It Has Been Shown Inmentioning

confidence: 99%

See 2 more Smart Citations

Fully Distributed Alternating Direction Method of Multipliers in Digraphs via Finite-Time Termination Mechanisms

Jiang,

Charalambous

2021

Preprint

Self Cite

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“…In this paper, we focus on distributed control and coordination over wireless networks nodes that are battery powered or utilize energy harvesting techniques. We focus on the average consensus problem in which a group of nodes reaches agreement to a common value that is equal to the average of the initial states of the nodes [9,16]. Calculating the average of their initial states allows nodes to coordinate their actions via a common decision and is useful in many applications such as load balancing, voting schemes, quantized privacy protocols (can be used as the basis for various encoding schemes), and distributed optimization.…”

Section: Introductionmentioning

confidence: 99%

Finite Time Exact Quantized Average Consensus with Limited Resources and Transmission Stopping for Energy-Aware Networks

Rikos¹,

Hadjicostis²,

Johansson³

2021

Preprint

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Composed of spatially distributed sensors and actuators that communicate through wireless networks, networked control systems are emerging as a fundamental infrastructure technology in 5G and IoT technologies, including diverse applications, such as autonomous vehicles, UAVs, and various sensing devices. In order to increase flexibility and reduce deployment and maintenance costs, many such applications consider battery-powered or energy-harvesting networks, which bring additional limitations on the energy consumption of the wireless network. Specifically, the operation of battery-powered or energyharvesting wireless communication networks needs to guarantee (i) efficient communication between nodes and (ii) preservation of available energy. Motivated by these novel requirements, in this paper, we present and analyze a novel distributed average consensus algorithm, which (i) operates exclusively on quantized values (in order to guarantee efficient communication and data storage), and (ii) relies on event-driven updates (in order to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). We characterize the properties of the proposed algorithm and show that its execution, on any time-invariant and strongly connected digraph, will allow all nodes to reach, in finite time, a common consensus value that is equal to the exact average (represented as the ratio of two quantized values). Furthermore, we show that our algorithm allows each node to cease transmissions once the exact average of the initial quantized values has been reached (in order to preserve its battery energy). Then, we present upper bounds on (i) the number of transmissions and computations each node has to perform during the execution of the algorithm, and (ii) the memory and energy requirements of each node in order for the algorithm to be executed. Finally, we provide examples that demonstrate the operation, performance, and potential advantages of our proposed algorithm.

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Invariant Properties and Bounds on a Finite Time Consensus Algorithm

Toulouse

Minh

2019

Transactions on Large-Scale Data- And Knowledge-Centered Systems XLI

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Decentralised minimum-time average consensus in digraphs

Cited by 13 publications

References 22 publications

Fully Distributed Alternating Direction Method of Multipliers in Digraphs via Finite-Time Termination Mechanisms

Fully Distributed Alternating Direction Method of Multipliers in Digraphs via Finite-Time Termination Mechanisms

Finite Time Exact Quantized Average Consensus with Limited Resources and Transmission Stopping for Energy-Aware Networks

Invariant Properties and Bounds on a Finite Time Consensus Algorithm

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