Optimal worst-case dynamic average consensus

Scoy, Bryan Van; Freeman, Randy A.; Lynch, Kevin

doi:10.1109/acc.2015.7172171

Cited by 8 publications

(4 citation statements)

References 16 publications

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“…In continuous time, the parameters may be scaled to achieve any desired convergence rate, while in discrete time the parameters must be carefully chosen to ensure convergence. The problem of optimizing the convergence rate has received significant attention in the literature [56,57,58,59,60,61,62,63,64,65]. Here, we give a simple method using root locus techniques for choosing the parameters in order to optimize the convergence rate.…”

Section: Discrete-time Dynamic Average Consensus Algorithmsmentioning

confidence: 99%

Tutorial on Dynamic Average Consensus: The Problem, Its Applications, and the Algorithms

et al. 2019

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Technological advances in ad-hoc networking and the availability of low-cost reliable computing, data storage and sensing devices have made possible scenarios where the coordination of many subsystems extends the range of human capabilities. Smart grid operations, smart transportation, smart healthcare and sensing networks for environmental monitoring and exploration in hazardous situations are just a few examples of such network operations. In these applications, the ability of a network system to, in a decentralized fashion, fuse information, compute common estimates of unknown quantities, and agree on a common view of the world is critical. These problems can be formulated as agreement problems on linear combinations of dynamically changing reference signals or local parameters. This dynamic agreement problem corresponds to dynamic average consensus, which is the problem of interest of this article. The dynamic average consensus problem is for a group of agents to cooperate in order to track the average of locally available time-varying reference signals, where each agent is only capable of local computations and communicating with local neighbors, see Figure 1. Figure 1: A group of communication agents, each endowed with a time-varying reference signal. 1 arXiv:1803.04628v2 [cs.SY] 24 Nov 2018 Centralized solutions have drawbacksThe difficulty in the dynamic average consensus problem is that the information is distributed across the network. A straightforward solution, termed centralized, to the dynamic average consensus problem appears to be to gather all of the information in a single place, do the computation (in other words, calculate the average), and then send the solution back through the network to each agent. Although simple, the centralized approach has numerous drawbacks: (1) the algorithm is not robust to failures of the centralized agent (if the centralized agent fails, then the entire computation fails), (2) the method is not scalable since the amount of communication and memory required on each agent scales with the size of the network, (3) each agent must have a unique identifier (so that the centralized agent counts each value only once), (4) the calculated average is delayed by an amount which grows with the size of the network, and (5) the reference signals from each agent are exposed over the entire network which is unacceptable in applications involving sensitive data. The centralized solution is fragile due to existence of a single failure point in the network. This can be overcome by having every agent act as the centralized agent. In this approach, referred to as flooding, agents transmit the values of the reference signals across the entire network until each agent knows each reference signal. This may be summarized as "first do all communications, then do all computations". While flooding fixes the issue of robustness to agent failures, it is still subject to many of the drawbacks of the centralized solution. Also, although this approach works reasonably well for small size networks,...

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Section: Discrete-time Dynamic Average Consensus Algorithmsmentioning

confidence: 99%

Tutorial on Dynamic Average Consensus: The Problem, Its Applications, and the Algorithms

et al. 2019

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“…In the case of (k) = 0, it follows from (18) that (k + 1) = (k) = 0 is ensured, and by invoking Lemma 1, it can be concluded that the matrix D i (k) is doubly stochastic. Moreover, dynamics of (k) can be derived immediately from (18), such that…”

Section: Distributed Gain Adaptation Of Adjacency Matrixmentioning

confidence: 99%

“…For instance, Freeman et al introduced the well‐studied Proportional and Proportional‐Integral (ie, PI) protocols coupled with undirected topology to solve this problem. Its effectiveness in power distribution is examined in the work of Zhang et al, its discrete enhancement with respect to time delays can be found in the work of Van Scoy et al, and a worst‐case robust average consensus was revealed in the other work of Van Scoy et al for an undirected graph using a polynomial liner protocol. Nosrati et al proposed a nonlinear protocol to solve the underlying problem under both undirected and balanced topologies.…”

Section: Introductionmentioning

confidence: 99%

Dynamic average consensus with topology balancing under a directed graph

Xin

Wang

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, the distributed average tracking problem is studied on the premise of a strongly connected directed graph. To this end, we propose a weight balance strategy that could potentially make the adjacency matrix doubly stochastic for any strongly connected directed graph. The proposed scheme is fully distributive with finite time convergence and we again prove that network connectivity (described by the first left eigenvector) is instrumental in networked control systems. Then, a discrete‐time average tracking observer is introduced to ensure that all networked systems can track the average of the reference signals with bounded error. Simulation results verify the effectiveness of the proposed methods.

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“…Meanwhile, more advanced design methods have been exploited to track time-varying references [13], sinusoid references with unknown frequencies [14], and arbitrary references with bounded derivatives [15]. Recently, the study on DAT has been expanded to handle complicated agent dynamics, e.g., double-integrator dynamics [16], [17], generic linear dynamics [8], [18], and nonlinear dynamics [19], [20], with performance analysis [21]- [23], privacy requirements [24], and for balanced directed networks [25], [26]. By introducing a "damping" factor, the algorithm of [27] ensures DAT with small errors while being robust against initialization errors.…”

Section: Introductionmentioning

confidence: 99%

Delay and Packet-Drop Tolerant Multi-Stage Distributed Average Tracking in Mean Square

Chen¹,

Changjiang²,

Guo³

et al. 2020

Preprint

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This paper studies the distributed average tracking problem pertaining to a discrete-time linear timeinvariant multi-agent network, which is subject to, concurrently, input delays, random packet-drops, and reference noise. The problem amounts to an integrated design of delay and packet-drop tolerant algorithm and determining the ultimate upper bound of the tracking error between agents' states and the average of the reference signals. The investigation is driven by the goal of devising a practically more attainable average tracking algorithm, thereby extending the existing work in the literature which largely ignored the aforementioned uncertainties. For this purpose, a blend of techniques from Kalman filtering, multi-stage consensus filtering, and predictive control is employed, which gives rise to a simple yet comepelling distributed average tracking algorithm that is robust to initialization error and allows the trade-off between communication/computation cost and stationary-state tracking error. Due to the inherent coupling among different control components, convergence analysis is significantly challenging. Nevertheless, it is revealed that the allowable values of the algorithm parameters rely upon the maximal degree of an expected network, while the convergence speed depends upon the second smallest eigenvalue of the same network's topology. The effectiveness of the theoretical results is verified by a numerical example.

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Optimal worst-case dynamic average consensus

Cited by 8 publications

References 16 publications

Tutorial on Dynamic Average Consensus: The Problem, Its Applications, and the Algorithms

Tutorial on Dynamic Average Consensus: The Problem, Its Applications, and the Algorithms

Dynamic average consensus with topology balancing under a directed graph

Delay and Packet-Drop Tolerant Multi-Stage Distributed Average Tracking in Mean Square

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