1,621 research outputs found
Average Consensus in the Presence of Delays and Dynamically Changing Directed Graph Topologies
Classical approaches for asymptotic convergence to the global average in a
distributed fashion typically assume timely and reliable exchange of
information between neighboring components of a given multi-component system.
These assumptions are not necessarily valid in practical settings due to
varying delays that might affect transmissions at different times, as well as
possible changes in the underlying interconnection topology (e.g., due to
component mobility). In this work, we propose protocols to overcome these
limitations. We first consider a fixed interconnection topology (captured by a
- possibly directed - graph) and propose a discrete-time protocol that can
reach asymptotic average consensus in a distributed fashion, despite the
presence of arbitrary (but bounded) delays in the communication links. The
protocol requires that each component has knowledge of the number of its
outgoing links (i.e., the number of components to which it sends information).
We subsequently extend the protocol to also handle changes in the underlying
interconnection topology and describe a variety of rather loose conditions
under which the modified protocol allows the components to reach asymptotic
average consensus. The proposed algorithms are illustrated via examples.Comment: 37 page
The Most Exigent Eigenvalue: Guaranteeing Consensus under an Unknown Communication Topology and Time Delays
This document aims to answer the question of what is the minimum delay value
that guarantees convergence to consensus for a group of second order agents
operating under different protocols, provided that the communication topology
is connected but unknown. That is, for all the possible communication
topologies, which value of the delay guarantees stability? To answer this
question we revisit the concept of most exigent eigenvalue, applying it to two
different consensus protocols for agents driven by second order dynamics. We
show how the delay margin depends on the structure of the consensus protocol
and the communication topology, and arrive to a boundary that guarantees
consensus for any connected communication topology. The switching topologies
case is also studied. It is shown that for one protocol the stability of the
individual topologies is sufficient to guarantee consensus in the switching
case, whereas for the other one it is not
A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays
Copyright @ 2012 Taylor & FrancisIn this article, the distributed consensus problem is considered for discrete-time delayed networks of dynamic agents with fixed topologies, where the networks under investigation are directed and the time-delays involved are distributed time delays including a single or multiple time delay(s) as special cases. By using the invariance principle of delay difference systems, a new unified framework is established to deal with the consensus for the discrete-time delayed multi-agent system. It is shown that the addressed discrete-time network with arbitrary distributed time delays reaches consensus provided that it is strongly connected. A numerical example is presented to illustrate the proposed methods.This work was supported in part by City University of Hong Kong under Grant 7008114, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 60774073 and 61074129, and the Natural Science Foundation of Jiangsu Province of China under Grant BK2010313
On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay
This paper studies the robustness of a dynamic average consensus algorithm to
communication delay over strongly connected and weight-balanced (SCWB)
digraphs. Under delay-free communication, the algorithm of interest achieves a
practical asymptotic tracking of the dynamic average of the time-varying
agents' reference signals. For this algorithm, in both its continuous-time and
discrete-time implementations, we characterize the admissible communication
delay range and study the effect of the delay on the rate of convergence and
the tracking error bound. Our study also includes establishing a relationship
between the admissible delay bound and the maximum degree of the SCWB digraphs.
We also show that for delays in the admissible bound, for static signals the
algorithms achieve perfect tracking. Moreover, when the interaction topology is
a connected undirected graph, we show that the discrete-time implementation is
guaranteed to tolerate at least one step delay. Simulations demonstrate our
results
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