600 research outputs found
A Combinatorial Necessary and Sufficient Condition for Cluster Consensus
In this technical note, cluster consensus of discrete-time linear multi-agent
systems is investigated. A set of stochastic matrices is said to
be a cluster consensus set if the system achieves cluster consensus for any
initial state and any sequence of matrices taken from . By
introducing a cluster ergodicity coefficient, we present an equivalence
relation between a range of characterization of cluster consensus set under
some mild conditions including the widely adopted inter-cluster common
influence. We obtain a combinatorial necessary and sufficient condition for a
compact set to be a cluster consensus set. This combinatorial
condition is an extension of the avoiding set condition for global consensus,
and can be easily checked by an elementary routine. As a byproduct, our result
unveils that the cluster-spanning trees condition is not only sufficient but
necessary in some sense for cluster consensus problems.Comment: 6 page
Coordinated Robot Navigation via Hierarchical Clustering
We introduce the use of hierarchical clustering for relaxed, deterministic
coordination and control of multiple robots. Traditionally an unsupervised
learning method, hierarchical clustering offers a formalism for identifying and
representing spatially cohesive and segregated robot groups at different
resolutions by relating the continuous space of configurations to the
combinatorial space of trees. We formalize and exploit this relation,
developing computationally effective reactive algorithms for navigating through
the combinatorial space in concert with geometric realizations for a particular
choice of hierarchical clustering method. These constructions yield
computationally effective vector field planners for both hierarchically
invariant as well as transitional navigation in the configuration space. We
apply these methods to the centralized coordination and control of
perfectly sensed and actuated Euclidean spheres in a -dimensional ambient
space (for arbitrary and ). Given a desired configuration supporting a
desired hierarchy, we construct a hybrid controller which is quadratic in
and algebraic in and prove that its execution brings all but a measure zero
set of initial configurations to the desired goal with the guarantee of no
collisions along the way.Comment: 29 pages, 13 figures, 8 tables, extended version of a paper in
preparation for submission to a journa
Symmetry-Induced Clustering in Multi-Agent Systems using Network Optimization and Passivity
This work studies the effects of a weak notion of symmetry on
diffusively-coupled multi-agent systems. We focus on networks comprised of
agents and controllers which are maximally equilibrium independent passive, and
show that these converge to a clustered steady-state, with clusters
corresponding to certain symmetries of the system. Namely, clusters are
computed using the notion of the exchangeability graph. We then discuss
homogeneous networks and the cluster synthesis problem, namely finding a graph
and homogeneous controllers forcing the agents to cluster at prescribed values.Comment: 7 pages, 4 figure
Distributed field estimation in wireless sensor networks
This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks
Distributed field estimation in wireless sensor networks
This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks
Distributed Detection and Estimation in Wireless Sensor Networks
In this article we consider the problems of distributed detection and
estimation in wireless sensor networks. In the first part, we provide a general
framework aimed to show how an efficient design of a sensor network requires a
joint organization of in-network processing and communication. Then, we recall
the basic features of consensus algorithm, which is a basic tool to reach
globally optimal decisions through a distributed approach. The main part of the
paper starts addressing the distributed estimation problem. We show first an
entirely decentralized approach, where observations and estimations are
performed without the intervention of a fusion center. Then, we consider the
case where the estimation is performed at a fusion center, showing how to
allocate quantization bits and transmit powers in the links between the nodes
and the fusion center, in order to accommodate the requirement on the maximum
estimation variance, under a constraint on the global transmit power. We extend
the approach to the detection problem. Also in this case, we consider the
distributed approach, where every node can achieve a globally optimal decision,
and the case where the decision is taken at a central node. In the latter case,
we show how to allocate coding bits and transmit power in order to maximize the
detection probability, under constraints on the false alarm rate and the global
transmit power. Then, we generalize consensus algorithms illustrating a
distributed procedure that converges to the projection of the observation
vector onto a signal subspace. We then address the issue of energy consumption
in sensor networks, thus showing how to optimize the network topology in order
to minimize the energy necessary to achieve a global consensus. Finally, we
address the problem of matching the topology of the network to the graph
describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R.
Chellapa and S. Theodoridis, Eds., Elsevier, 201
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