Consensus Algorithms In Networks Research Articles

Distributed Finite-Time Termination for Consensus Algorithm in Switching Topologies

In this article, we present a finite-time stopping criterion for consensus algorithms in networks with dynamic communication topology. Prior state of the art has established convergence to the consensus value; however, the asymptotic convergence of these algorithms poses a challenge in practical settings where the response from agents is required in finite time. To this end, we propose a maximum-minimum protocol that propagates the global maximum and minimum values of agent states (while running the consensus algorithm) in the network. This article focuses on establishing that the global maximum and minimum values are strictly monotonic even for a dynamic topology, and they can be used to distributively ascertain the closeness to convergence in finite time. We rigorously show that each node can have access to the global maximum and minimum by running the proposed maximum-minimum protocol to realize a finite-time stopping criterion for the otherwise asymptotic consensus algorithm. The practical utility of the algorithm is illustrated through experiments where each agent is instantiated by a NodeJS <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">socket.io</i> server.

Consensus in Networks of Multiagents with Stochastically Switching Topologies and Time-Varying Delays

In this paper, we investigated a very general model of discrete-time consensus algorithm in networks of multiagents with stochastically switching topologies and bounded time-varying delays. Here no...

Distributed Binary Consensus in Networks with Disturbances

This article evaluates convergence rates of binary majority consensus algorithms in networks with different types of disturbances and studies the potential capacity of randomization to foster convergence. Simulation results show that (a) additive noise, topology randomness, and stochastic message loss may improve the convergence rate; (b) presence of faulty nodes degrades the convergence rate; and (c) explicit randomization of consensus algorithms can be exploited to improve the convergence rate. Watts-Strogatz and Waxman graphs are used as underlying network topologies. A consensus algorithm is proposed that exchanges state information with dynamically randomly selected neighbors and, through this randomization, achieves almost sure convergence in some scenarios.

Consensus and Coherence in Fractal Networks

We consider first- and second-order consensus algorithms in networks with stochastic disturbances. We quantify the deviation from consensus using the notion of network coherence, which can be expressed as an $H_{2}$ norm of the stochastic system. We use the setting of fractal networks to investigate the question of whether a purely topological measure, such as the fractal dimension, can capture the asymptotics of coherence in the large system size limit. Our analysis for first-order systems is facilitated by connections between first-order stochastic consensus and the global mean first passage time of random walks. We then show how to apply similar techniques to analyze second-order stochastic consensus systems. Our analysis reveals that two networks with the same fractal dimension can exhibit different asymptotic scalings for network coherence. Thus, this topological characterization of the network does not uniquely determine coherence behavior. The question of whether the performance of stochastic consensus algorithms in large networks can be captured by purely topological measures, such as the spatial dimension, remains open.

Dynamic average consensus under limited control authority and privacy requirements

SummaryThis paper introduces a novel continuous‐time dynamic average consensus algorithm for networks whose interaction is described by a strongly connected and weight‐balanced directed graph. The proposed distributed algorithm allows agents to track the average of their dynamic inputs with some steady‐state error whose size can be controlled using a design parameter. This steady‐state error vanishes for special classes of input signals. We analyze the asymptotic correctness of the algorithm under time‐varying interaction topologies and characterize the requirements on the stepsize for discrete‐time implementations. We show that our algorithm naturally preserves the privacy of the local input of each agent. Building on this analysis, we synthesize an extension of the algorithm that allows individual agents to control their own rate of convergence towards agreement and handle saturation bounds on the driving command. Finally, we show that the proposed extension additionally preserves the privacy of the transient response of the agreement states and the final agreement value from internal and external adversaries. Numerical examples illustrate the results. Copyright © 2014 John Wiley &amp; Sons, Ltd.

A Sufficient Condition for Convergence of Sampled-Data Consensus for Double-Integrator Dynamics With Nonuniform and Time-Varying Communication Delays

This technical note investigates a discrete-time second-order consensus algorithm for networks of agents with nonuniform and time-varying communication delays under dynamically changing communication topologies in a sampled-data setting. Some new proof techniques are proposed to perform the convergence analysis. It is finally shown that under certain assumptions upon the velocity damping gain and the sampling period, consensus is achieved for arbitrary bounded time-varying communication delays if the union of the associated digraphs of the interaction matrices in the presence of delays has a directed spanning tree frequently enough.

Robustness of Consensus Algorithms for Networks with Communication Delays and Switching Topology

Robustness of Consensus Algorithms for Networks with Communication Delays and Switching Topology

Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays

We analyze stability of consensus algorithms in networks of multi-agents with time-varying topologies and delays. The topology and delays are modeled as induced by an adapted process and are rather general, including i.i.d.\ topology processes, asynchronous consensus algorithms, and Markovian jumping switching. In case the self-links are instantaneous, we prove that the network reaches consensus for all bounded delays if the graph corresponding to the conditional expectation of the coupling matrix sum across a finite time interval has a spanning tree almost surely. Moreover, when self-links are also delayed and when the delays satisfy certain integer patterns, we observe and prove that the algorithm may not reach consensus but instead synchronize at a periodic trajectory, whose period depends on the delay pattern. We also give a brief discussion on the dynamics in the absence of self-links.

Consensus and Synchronization in Delayed Networks of Mobile Multi-agents

AbstractThe stability of consensus algorithms in networks of mobile multi-agents with transmission delays is investigated. The movements of agents are modeled by the random waypoint (RWP) model. Thus, the communication topology is modeled as induced by a homogeneous Markov chain. It is found that, under several conditions, the stability dynamics are dramatically influenced by the delay patterns. In the case where self-links exist and are instantaneous, consensus is reached if the expectation of the graph topology has a spanning tree; in the other case where the self-links have delays and only integer delays with certain patterns are possible, the algorithm does not reach consensus but instead synchronizes at a periodic trajectory, whose period depends on the delay patterns. The dynamics in the absence of self-links exhibit similar phenomena. The theoretical results are verified in a network of RWP mobile agents.