7,535 research outputs found
Prediction error identification of linear dynamic networks with rank-reduced noise
Dynamic networks are interconnected dynamic systems with measured node
signals and dynamic modules reflecting the links between the nodes. We address
the problem of \red{identifying a dynamic network with known topology, on the
basis of measured signals}, for the situation of additive process noise on the
node signals that is spatially correlated and that is allowed to have a
spectral density that is singular. A prediction error approach is followed in
which all node signals in the network are jointly predicted. The resulting
joint-direct identification method, generalizes the classical direct method for
closed-loop identification to handle situations of mutually correlated noise on
inputs and outputs. When applied to general dynamic networks with rank-reduced
noise, it appears that the natural identification criterion becomes a weighted
LS criterion that is subject to a constraint. This constrained criterion is
shown to lead to maximum likelihood estimates of the dynamic network and
therefore to minimum variance properties, reaching the Cramer-Rao lower bound
in the case of Gaussian noise.Comment: 17 pages, 5 figures, revision submitted for publication in
Automatica, 4 April 201
Statistical description of the black hole degeneracy spectrum
We use mathematical methods based on generating functions to study the
statistical properties of the black hole degeneracy spectrum in loop quantum
gravity. In particular we will study the persistence of the observed effective
quantization of the entropy as a function of the horizon area. We will show
that this quantization disappears as the area increases despite the existence
of black hole configurations with a large degeneracy. The methods that we
describe here can be adapted to the study of the statistical properties of the
black hole degeneracy spectrum for all the existing proposals to define black
hole entropy in loop quantum gravity.Comment: 41 pages, 12 figure
Global sensitivity analysis for the boundary control of an open channel
The goal of this paper is to solve the global sensitivity analysis for a
particular control problem. More precisely, the boundary control problem of an
open-water channel is considered, where the boundary conditions are defined by
the position of a down stream overflow gate and an upper stream underflow gate.
The dynamics of the water depth and of the water velocity are described by the
Shallow Water equations, taking into account the bottom and friction slopes.
Since some physical parameters are unknown, a stabilizing boundary control is
first computed for their nominal values, and then a sensitivity anal-ysis is
performed to measure the impact of the uncertainty in the parameters on a given
to-be-controlled output. The unknown physical parameters are de-scribed by some
probability distribution functions. Numerical simulations are performed to
measure the first-order and total sensitivity indices
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