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Convergence Speed in Distributed consensus and Averaging

SIAM REVIEW 2011年第4期53卷 747-772页

作者： Olshevsky, Alex Tsitsiklis, John N. Princeton Univ Dept Mech & Aerosp Engn Princeton NJ 08544 USA MIT Informat & Decis Syst Lab Cambridge MA 02139 USA

We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worst-case convergence time for various classes of linear, time-invariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a time-varying topology, and provide a polynomial-time averaging algorithm.

关键词： consensus algorithms distributed averaging cooperative control

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Impact of consensus contours from multiple PET segmentation methods on the accuracy of functional volume delineation

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EUROPEAN JOURNAL OF NUCLEAR MEDICINE AND MOLECULAR IMAGING 2016年第5期43卷 911-924页

作者： Schaefer, A. Vermandel, M. Baillet, C. Dewalle-Vignion, A. S. Modzelewski, R. Vera, P. Massoptier, L. Parcq, C. Gibon, D. Fechter, T. Nemer, U. Gardin, I. Nestle, U. Univ Saarland Dept Nucl Med Med Ctr D-66421 Homburg Germany Univ Lille INSERM CHU Lille U1189ONCO THAI Image Assisted Laser Therapy Onco F-59000 Lille France CHU Lille Dept Nucl Med F-59000 Lille France Ctr Henri Becquerel F-76000 Rouen France LITIS EA4108 F-76000 Rouen France AQUILAB Res & Innovat Dept F-59120 Loos Les Lille France Univ Med Ctr Freiburg Dept Radiat Oncol Freiburg Germany German Canc Consortium DKTK Freiburg Heidelberg Germany German Canc Res Ctr Freiburg Germany Univ Med Ctr Freiburg Dept Nucl Med Freiburg Germany

Purpose The aim of this study was to evaluate the impact of consensus algorithms on segmentation results when applied to clinical PET images. In particular, whether the use of the majority vote or STAPLE algorithm could improve the accuracy and reproducibility of the segmentation provided by the combination of three semiautomatic segmentation algorithms was investigated. Methods Three published segmentation methods (contrast-oriented, possibility theory and adaptive thresholding) and two consensus algorithms (majority vote and STAPLE) were implemented in a single software platform (ArtiviewA (R)). Four clinical datasets including different locations (thorax, breast, abdomen) or pathologies (primary NSCLC tumours, metastasis, lymphoma) were used to evaluate accuracy and reproducibility of the consensus approach in comparison with pathology as the ground truth or CT as a ground truth surrogate. Results Variability in the performance of the individual segmentation algorithms for lesions of different tumour entities reflected the variability in PET images in terms of resolution, contrast and noise. Independent of location and pathology of the lesion, however, the consensus method resulted in improved accuracy in volume segmentation compared with the worst-performing individual method in the majority of cases and was close to the best-performing method in many cases. In addition, the implementation revealed high reproducibility in the segmentation results with small changes in the respective starting conditions. There were no significant differences in the results with the STAPLE algorithm and the majority vote algorithm. Conclusion This study showed that combining different PET segmentation methods by the use of a consensus algorithm offers robustness against the variable performance of individual segmentation methods and this approach would therefore be useful in radiation oncology. It might also be relevant for other scenarios such as the merging of expert recommendat

关键词： PET image segmentation consensus algorithms STAPLE Radiation oncology F-18-FDG PET Image segmentation

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Dynamic average consensus via nonlinear protocols

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AUTOMATICA 2012年第9期48卷 2262-2270页

作者： Nosrati, Shahram Shafiee, Masoud Menhaj, Mohammad Bagher Amirkabir Univ Technol Dept Elect Engn Tehran Iran

This paper addresses the dynamic average consensus problem under nonlinear protocols for networks of dynamic agents. In this problem, each agent aims to track the average of time-varying reference inputs of all the agents in the network by local communication with neighbors. We propose a class of continuous-time nonlinear protocols for this problem, and theoretical analyses for two cases are provided: (1) undirected networks with switching topologies and (2) balanced directed networks with switching topologies. Based upon the analysis results, design procedures for nonlinear protocols are presented. Simulations are also provided to demonstrate the effectiveness of the proposed design procedures. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： consensus algorithms Multi-agent systems Cooperative control

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consensus-Based Distributed Formation Control of Multi-Quadcopter Systems: Barrier Lyapunov Function Approach

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IEEE ACCESS 2023年 11卷 142916-142930页

作者： Sadeghzadeh-Nokhodberiz, Nargess Meskin, Nader Qom Univ Technol Dept Elect & Comp Engn Qom *** Iran Qatar Univ Dept Elect Engn Doha Qatar

The problem of formation tracking control for a group of quadcopters with nonlinear dynamics using Barrier Lyapunov Functions (BLFs) is studied in this paper where the quadcopters are following a desired predefined trajectory in a predefined formation shape. The BLFs are employed to formulate the problem of formation trajectory tracking with a predefined accuracy. For this purpose, logarithmic BLFs including both the trajectory errors and the errors between the quadcopters' distances with the desired ones (for the formation goal) are proposed. The method is firstly developed in a centralized scheme and then extended to a distributed framework using appropriate asymptotically convergent consensus algorithms. Therefore, the asymptotic convergence of the designed distributed algorithm to the centralized one is guaranteed. Moreover, due to the under-actuated feature of a quadcopter system, a general hierarchical scheme is considered for designing the controller. To this end, firstly a formation altitude tracking control is designed and then using the generated control signal, the formation translational tracking control is developed with the assumption of virtual inputs which are then employed to generate desired trajectory signals for the attitude control subsystem. Finally, attitude controllers are designed separately for each agent using the generated desired signals through logarithmic BLFs to consider a predefined accuracy. The efficiency of the proposed method is demonstrated through simulations and comparisons with the similar approaches in MATLAB-Simulink environment.

关键词： Formation tracking control multi-quadcopter system Barrier Lyapunov function (BLF) consensus algorithms

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consensus-based distributed dynamic sensor selection in decentralised sensor networks using the posterior Cramer-Rao lower bound

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SIGNAL PROCESSING 2015年 108卷 558-575页

作者： Mohammadi, Arash Asif, Amir Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 2J7 Canada Concordia Univ Dept Elect & Comp Engn Montreal PQ H3G 2W1 Canada

The paper considers the problem of dynamic sensor scheduling for non-linear tracking problems in distributed sensor/agent networks (AN/SN), where channel limitations restrict how many sensors can simultaneously participate in the estimation mechanism. Commonly referred to as sensor selection, the basic objective is to select a subset of sensors from available sensors that minimises the estimation error. The posterior Cramer-Rao lower bound (PCRLB) has recently been proposed as an effective sensor selection criteria. Nevertheless, existing PCRLB-based selectors are limited to centralised and hierarchical networks, and when extended to distributed architectures use approximate expressions. First, the non-conditional distributed PCRLB (dPCRLB) that considers observations and state variables to be random is used to derive the non-conditional sensor-selector. The dPCRLB expressions we derive are optimal. Unlike the non-conditional PCRLB, its conditional counterpart is a function of the past history of observations and is a more accurate representation of the system's performance. Second, the paper generalises the non-conditional dPCRLB sensor-selector to its conditional dPCRLB version. Both dPCRLB sensor-selectors use raw observations adding significant communication overhead. Third, the paper extends the conditional dPCRLB framework to quantised observations and develops the quantised version of the conditional dPCRLB sensor-selector. Numerical simulations verify the efficiency of our distributed dynamic sensor-selectors. (C) 2014 Elsevier B.V. All rights reserved.

关键词： consensus algorithms Distributed signal processing Data fusion for non-linear dynamical systems Posterior Cramer-Rao lower bound (PCRLB) Sensor selection Wireless sensor networks

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A simple consensus algorithm for distributed averaging in random geographical networks

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PRAMANA-JOURNAL OF PHYSICS 2012年第3期79卷 493-499页

作者： Jalili, Mahdi Sharif Univ Technol Dept Comp Engn Tehran Iran

Random geographical networks are realistic models for wireless sensor networks which are used in many applications. Achieving average consensus is very important in sensor networks and the faster the consensus is, the durable the sensors' life, and thus, the better the performance of the network. In this paper we compared the performance of a number of linear consensus algorithms with application to distributed averaging in random geographical networks. Interestingly, the simplest algorithm - where only the degree of receiving nodes is needed for the averaging - had the best performance in terms of the consensus time. Furthermore, we proved that the network has guaranteed convergence with this simple algorithm.

关键词： Sensor networks random geographical networks distributed averaging consensus algorithms

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Bipartite consensus in coupled harmonic oscillators with local instantaneous interaction and measurement noise

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IET CIRCUITS DEVICES & SYSTEMS 2022年第6期16卷 471-482页

作者： Wang, Zhaoyan Li, Hengyu Liu, Jun Zhang, Tiehui Ma, Xinru Xie, Shaorong Luo, Jun Jining Univ Sch Math & Comp Applicat Technol Qufu Shandong Peoples R China Shanghai Univ Sch Mechatron Engn & Automat Shanghai Peoples R China Jining Univ Coll Elementary Educ Qufu Shandong Peoples R China Chongqing Univ Coll Mech & Vehicle Engn Chongqing Peoples R China

This paper investigates the issue of bipartite consensus for coupled harmonic oscillators under the cooperation-competition network topology while considering measurement noise. The concept of bipartite consensus in mean square is established for networked harmonic oscillator systems. In this sense, two consensus algorithms that only use sampled velocity data on the agents in a network are given. Based on the specific structure of the Laplacian matrix related to the cooperation-competition network topology, some sufficient conditions are given to ensure the realisation of the bipartite consensus of the coupled harmonic oscillators. Finally, three examples are provided to illustrate the corresponding theoretical results.

关键词： network theory (graphs) measurement noise consensus algorithms cooperation-competition network topology least mean squares methods coupled harmonic oscillators local instantaneous interaction Laplacian matrix networked harmonic oscillator systems bipartite consensus matrix algebra harmonic oscillators

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Accurate Distributed Secondary Control for DC Microgrids Considering Communication Delays: A Surplus consensus-Based Approach

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IEEE TRANSACTIONS ON SMART GRID 2022年第3期13卷 1709-1719页

作者： Du, Yuhua Lu, Xiaonan Tang, Wenyuan Temple Univ Coll Engn Philadelphia PA 19122 USA North Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27695 USA

The state-of-the-art dynamic consensus-based microgrid (MG) secondary controls suffer from the communication delay effect. Specifically, the system could not converge to the desired operating points with time-delayed communications. Such deviations are hard to detect in a decentralized manner and could destabilize the system. This paper proposes an accurate distributed secondary controller for DC MGs based on the surplus consensus algorithm. The proposed controller achieves accurate proportional power sharing and average voltage regulation among distributed generators (DGs) with the presence of variable and bounded communication delays. A surplus consensus-based observer is developed. The developed observer is proved robust against variable and bounded communication delays;it tracks the average of a group of dynamic states with zero steady-state deviations, which cannot be done using the conventional dynamic consensus-based observer. The convergence speed of the developed observer is analyzed and a parameter design procedure is presented. Moreover, the delay-dependent stability analysis of DC MG operation with the proposed secondary controller is derived. The marginal delay that leads the system to instability is calculated. At last, the performance of the proposed secondary controller and the developed stability analysis are validated under various scenarios using MATLAB/Simulink.

关键词： Delays Observers Voltage control Stability analysis Regulation Delay effects Steady-state Communication delay consensus algorithms DC microgrid distributed control secondary control surplus consensus

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Discrete-time dynamic average consensus

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AUTOMATICA 2010年第2期46卷 322-329页

作者： Zhu, Minghui Martinez, Sonia Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

We propose a class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs. The convergence results rely on the input-to-output stability properties of static average consensus algorithms and require that the union of communication graphs over a bounded period of time be strongly connected. The only requirement on the set of reference inputs is that the maximum relative deviation between the nth-order differences of any two reference inputs be bounded for some integer n >= 1. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： consensus algorithms Multi-agent systems Cooperative control

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consensus Over Random Graph Processes: Network Borel-Cantelli Lemmas for Almost Sure Convergence

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第10期61卷 5690-5707页

作者： Shi, Guodong Anderson, Brian D. O. Johansson, Karl Henrik Australian Natl Univ Coll Engn & Comp Sci Res Sch Engn Canberra ACT 0200 Australia NICTA Canberra ACT 2601 Australia KTH Royal Inst Technol ACCESS Linnaeus Ctr S-10044 Stockholm Sweden

Distributed consensus computation over random graph processes is considered. The random graph process is defined as a sequence of random variables which take values from the set of all possible digraphs over the node set. At each time step, every node updates its state based on a Bernoulli trial, independent in time and among different nodes: either averaging among the neighbor set generated by the random graph, or sticking with its current state. The connectivity-independence and arc-independence are introduced to capture the fundamental influence of the random graphs on the consensus convergence. Necessary and/or sufficient conditions are presented on the success probabilities of the Bernoulli trials for the network to reach a global almost sure consensus, with some sharp threshold established revealing a consensus zero-one law. Convergence rates are established by the lower and upper bounds of the epsilon-computation time. We also generalize the concepts of connectivity/arc independence to their analogues from the *-mixing point of view, so that our results apply to a very wide class of graphical models, including the majority of random graph models in the literature, e.g., Erdos-Renyi, gossiping, and Markovian random graphs. We show that under *-mixing, our convergence analysis continues to hold and the corresponding almost sure consensus conditions are established. Finally, we further investigate almost sure finite-time convergence of random gossiping algorithms, and prove that the Bernoulli trials play a key role in ensuring finite-time convergence. These results add to the understanding of the interplay between random graphs, random computations, and convergence probability for distributed information processing.

关键词： consensus algorithms random graphs zero-one law gossiping

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