82 research outputs found
On the Quality of Wireless Network Connectivity
Despite intensive research in the area of network connectivity, there is an
important category of problems that remain unsolved: how to measure the quality
of connectivity of a wireless multi-hop network which has a realistic number of
nodes, not necessarily large enough to warrant the use of asymptotic analysis,
and has unreliable connections, reflecting the inherent unreliable
characteristics of wireless communications? The quality of connectivity
measures how easily and reliably a packet sent by a node can reach another
node. It complements the use of \emph{capacity} to measure the quality of a
network in saturated traffic scenarios and provides a native measure of the
quality of (end-to-end) network connections. In this paper, we explore the use
of probabilistic connectivity matrix as a possible tool to measure the quality
of network connectivity. Some interesting properties of the probabilistic
connectivity matrix and their connections to the quality of connectivity are
demonstrated. We argue that the largest eigenvalue of the probabilistic
connectivity matrix can serve as a good measure of the quality of network
connectivity.Comment: submitted to IEEE INFOCOM 201
Matrix Design for Optimal Sensing
We design optimal () matrices, with unit columns, so that
the maximum condition number of all the submatrices comprising 3 columns is
minimized. The problem has two applications. When estimating a 2-dimensional
signal by using only three of observations at a given time, this minimizes
the worst-case achievable estimation error. It also captures the problem of
optimum sensor placement for monitoring a source located in a plane, when only
a minimum number of required sensors are active at any given time. For
arbitrary , we derive the optimal matrices which minimize the maximum
condition number of all the submatrices of three columns. Surprisingly, a
uniform distribution of the columns is \emph{not} the optimal design for odd
.Comment: conferenc
Certifying non-existence of undesired locally stable equilibria in formation shape control problems
A fundamental control problem for autonomous vehicle formations is formation
shape control, in which the agents must maintain a prescribed formation shape
using only information measured or communicated from neighboring agents. While
a large and growing literature has recently emerged on distance-based formation
shape control, global stability properties remain a significant open problem.
Even in four-agent formations, the basic question of whether or not there can
exist locally stable incorrect equilibrium shapes remains open. This paper
shows how this question can be answered for any size formation in principle
using semidefinite programming techniques for semialgebraic problems, involving
solutions sets of polynomial equations, inequations, and inequalities.Comment: 6 pages; to appear in the 2013 IEEE Multiconference on Systems and
Contro
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