55 research outputs found
On Convergence Rate of Scalar Hegselmann-Krause Dynamics
In this work, we derive a new upper bound on the termination time of the
Hegselmann-Krause model for opinion dynamics. Using a novel method, we show
that the termination rate of this dynamics happens no longer than
which improves the best known upper bound of by a factor of .Comment: 5 pages, 2 figures, submitted to The American Control Conference,
Sep. 201
An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each pair of nodes is able to
communicate with each other directly and reliably. We consider the mobile
Byzantine fault model proposed by Garay '94 -- in the model, an omniscient
adversary can corrupt up to nodes in each round, and at the beginning of
each round, faults may "move" in the system (i.e., different sets of nodes may
become faulty in different rounds). Recent work by Bonomi et al. '16 proposed a
simple iterative approximate consensus algorithm which requires at least
nodes. This paper proposes a novel technique of using "confession" (a mechanism
to allow others to ignore past behavior) and a variant of reliable broadcast to
improve the fault-tolerance level. In particular, we present an approximate
consensus algorithm that requires only nodes, an
improvement over the state-of-the-art algorithms.
Moreover, we also show that the proposed algorithm is optimal within a family
of round-based algorithms
Optimal strategies in the average consensus problem
We prove that for a set of communicating agents to compute the average of
their initial positions (average consensus problem), the optimal topology of
communication is given by a de Bruijn's graph. Consensus is then reached in a
finitely many steps. A more general family of strategies, constructed by block
Kronecker products, is investigated and compared to Cayley strategies.Comment: 9 pages; extended preprint with proofs of a CDC 2007 (Conference on
decision and Control) pape
Iterative Approximate Consensus in the presence of Byzantine Link Failures
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each directed link of the underlying
communication graph represents a communication channel between a pair of nodes.
We adopt the transient Byzantine link failure model [15, 16], where an
omniscient adversary controls a subset of the directed communication links, but
the nodes are assumed to be fault-free.
Recent work has addressed the problem of reaching approximate consen- sus in
incomplete graphs with Byzantine nodes using a restricted class of iterative
algorithms that maintain only a small amount of memory across iterations [22,
21, 23, 12]. However, to the best of our knowledge, we are the first to
consider approximate consensus in the presence of Byzan- tine links. We extend
our past work that provided exact characterization of graphs in which the
iterative approximate consensus problem in the presence of Byzantine node
failures is solvable [22, 21]. In particular, we prove a tight necessary and
sufficient condition on the underlying com- munication graph for the existence
of iterative approximate consensus algorithms under transient Byzantine link
model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609
Asynchronous Convex Consensus in the Presence of Crash Faults
This paper defines a new consensus problem, convex consensus. Similar to
vector consensus [13, 20, 19], the input at each process is a d-dimensional
vector of reals (or, equivalently, a point in the d-dimensional Euclidean
space). However, for convex consensus, the output at each process is a convex
polytope contained within the convex hull of the inputs at the fault-free
processes. We explore the convex consensus problem under crash faults with
incorrect inputs, and present an asynchronous approximate convex consensus
algorithm with optimal fault tolerance that reaches consensus on an optimal
output polytope. Convex consensus can be used to solve other related problems.
For instance, a solution for convex consensus trivially yields a solution for
vector consensus. More importantly, convex consensus can potentially be used to
solve other more interesting problems, such as convex function optimization [5,
4].Comment: A version of this work is published in PODC 201
A Result On Implicit Consensus with Application to Emissions Control
This paper is concerned with a class of decentralised
control problems that arise in contemporary applications
where agents cooperate to control and regulate a global
quantity, are limited in the manner in which they communicate
with each other, and are required to reach consensus on some
implicit variable (for instance, CO2 emissions). An algorithm
is presented for achieving this goal. A simplified application of
the algorithm to emissions control for a fleet of Plug-in Hybrid
Electric Vehicles (PHEVs) is given
An Eulerian Approach to the Analysis of Krause's Consensus Models
Abstract. In this paper we analyze a class of multi-agent consensus dynamical systems inspired by Krause’s original model. As in Krause’s, the basic assumption is the so-called bounded confidence: two agents can influence each other only when their state values are below a given distance threshold R. We study the system under an Eulerian point of view considering (possibly continuous) probability distributions of agents and we present original convergence results. The limit distribution is always necessarily a convex combination of delta functions at least R far apart from each other: in other terms these models are locally aggregating. The Eulerian perspective provides the natural framework for designing a numerical algorithm, by which we obtain several simulations in 1 and 2 dimensions
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