79 research outputs found
An Upper Bound on the Convergence Time for Quantized Consensus of Arbitrary Static Graphs
We analyze a class of distributed quantized consensus algorithms for
arbitrary static networks. In the initial setting, each node in the network has
an integer value. Nodes exchange their current estimate of the mean value in
the network, and then update their estimation by communicating with their
neighbors in a limited capacity channel in an asynchronous clock setting.
Eventually, all nodes reach consensus with quantized precision. We analyze the
expected convergence time for the general quantized consensus algorithm
proposed by Kashyap et al \cite{Kashyap}. We use the theory of electric
networks, random walks, and couplings of Markov chains to derive an upper bound for the expected convergence time on an arbitrary graph of size
, improving on the state of art bound of for quantized consensus
algorithms. Our result is not dependent on graph topology. Example of complete
graphs is given to show how to extend the analysis to graphs of given topology.Comment: to appear in IEEE Trans. on Automatic Control, January, 2015. arXiv
admin note: substantial text overlap with arXiv:1208.078
Distributed Average Consensus under Quantized Communication via Event-Triggered Mass Summation
We study distributed average consensus problems in multi-agent systems with
directed communication links that are subject to quantized information flow.
The goal of distributed average consensus is for the nodes, each associated
with some initial value, to obtain the average (or some value close to the
average) of these initial values. In this paper, we present and analyze a
distributed averaging algorithm which operates exclusively with quantized
values (specifically, the information stored, processed and exchanged between
neighboring agents is subject to deterministic uniform quantization) and relies
on event-driven updates (e.g., to reduce energy consumption, communication
bandwidth, network congestion, and/or processor usage). We characterize the
properties of the proposed distributed averaging protocol on quantized values
and show that its execution, on any time-invariant and strongly connected
digraph, will allow all agents to reach, in finite time, a common consensus
value represented as the ratio of two integer that is equal to the exact
average. We conclude with examples that illustrate the operation, performance,
and potential advantages of the proposed algorithm
Broadcast Gossip Algorithms for Consensus on Strongly Connected Digraphs
We study a general framework for broadcast gossip algorithms which use
companion variables to solve the average consensus problem. Each node maintains
an initial state and a companion variable. Iterative updates are performed
asynchronously whereby one random node broadcasts its current state and
companion variable and all other nodes receiving the broadcast update their
state and companion variable. We provide conditions under which this scheme is
guaranteed to converge to a consensus solution, where all nodes have the same
limiting values, on any strongly connected directed graph. Under stronger
conditions, which are reasonable when the underlying communication graph is
undirected, we guarantee that the consensus value is equal to the average, both
in expectation and in the mean-squared sense. Our analysis uses tools from
non-negative matrix theory and perturbation theory. The perturbation results
rely on a parameter being sufficiently small. We characterize the allowable
upper bound as well as the optimal setting for the perturbation parameter as a
function of the network topology, and this allows us to characterize the
worst-case rate of convergence. Simulations illustrate that, in comparison to
existing broadcast gossip algorithms, the approaches proposed in this paper
have the advantage that they simultaneously can be guaranteed to converge to
the average consensus and they converge in a small number of broadcasts.Comment: 30 pages, submitte
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