94 research outputs found
Minimum Input Selection for Structural Controllability
Given a linear system , where is an matrix
with nonzero entries, we consider the problem of finding the smallest set
of state variables to affect with an input so that the resulting system is
structurally controllable. We further assume we are given a set of "forbidden
state variables" which cannot be affected with an input and which we have
to avoid in our selection. Our main result is that this problem can be solved
deterministically in operations
Consensus with Ternary Messages
We provide a protocol for real-valued average consensus by networks of agents
which exchange only a single message from the ternary alphabet {-1,0,1} between
neighbors at each step. Our protocol works on time-varying undirected graphs
subject to a connectivity condition, has a worst-case convergence time which is
polynomial in the number of agents and the initial values, and requires no
global knowledge about the graph topologies on the part of each node to
implement except for knowing an upper bound on the degrees of its neighbors
Distributed optimization over time-varying directed graphs
We consider distributed optimization by a collection of nodes, each having
access to its own convex function, whose collective goal is to minimize the sum
of the functions. The communications between nodes are described by a
time-varying sequence of directed graphs, which is uniformly strongly
connected. For such communications, assuming that every node knows its
out-degree, we develop a broadcast-based algorithm, termed the
subgradient-push, which steers every node to an optimal value under a standard
assumption of subgradient boundedness. The subgradient-push requires no
knowledge of either the number of agents or the graph sequence to implement.
Our analysis shows that the subgradient-push algorithm converges at a rate of
, where the constant depends on the initial values at the
nodes, the subgradient norms, and, more interestingly, on both the consensus
speed and the imbalances of influence among the nodes
On symmetric continuum opinion dynamics
This paper investigates the asymptotic behavior of some common opinion
dynamic models in a continuum of agents. We show that as long as the
interactions among the agents are symmetric, the distribution of the agents'
opinion converges. We also investigate whether convergence occurs in a stronger
sense than merely in distribution, namely, whether the opinion of almost every
agent converges. We show that while this is not the case in general, it becomes
true under plausible assumptions on inter-agent interactions, namely that
agents with similar opinions exert a non-negligible pull on each other, or that
the interactions are entirely determined by their opinions via a smooth
function.Comment: 28 pages, 2 figures, 3 file
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