Page 141 - Electrical Engineering Dictionary

closed-loop optimal control operation only increase an object. See dilation, erosion,
or structure of the controller with the deci- morphological filter, structuring element.
sion mechanism which, under uncertainty,
uses in the best possible way — with respect closing/opening filter one of an impor-
toagiven a priori criterion — all informa- tant class of morphological filters. Let γ
tion available to the controller; in particular, and ϕ be opening and closing operators re-
the closed-loop optimal control takes into ac- spectively. The following operators can be
count all future time instants at which new obtained by composing γ and ϕ (i.e., by ap-
decisions will be made; the best known ex- plying them in succession): γϕ, ϕγ , γϕγ ,
ample of a closed-loop optimal control rule is and ϕγ ϕ. These are all morphological fil-
the solution of the linear-quadratic-Gaussian ters, and collectively they are called clos-
problem (LQG problem). ing/opening filters or opening/closing filters.
No further operators can be obtained by com-
posing γ and ϕ. See closing, morphological
closed-loop system any system having filter, opening.
two separate paths inside it. The first path
conducts the signal flow from the input of that
clothes pin slang for a wood or plastic clip
system to the output of that same system. The
used to secure a blanket to conductors.
second path conducts the signal flow from the
output to the input of the system, thus estab-
CLT See central limit theorem.
lishing a feedback loop for the system. See
the figure below for a general description of a
cluster a group of data points on a space
closed-loop system. The forward and back-
or a group of communicating computer ma-
chines. A cluster of computers on a local
network can be installed to provide their ser-
vice as a unique computer. This is frequently
used for building large data storage and Web
servers. In computer disks, a cluster consists
of a fixed number of sectors. Each sector
contains several bytes, for example 512.

cluster analysis in pattern recognition,
the unsupervised analysis of samples to clus-
A closed-loop system.
ter them into classes based on (a) a distance
metric and (b) a clustering algorithm. Typ-
ward signal path construct the closed loop,
ical algorithms minimize a cluster criterion
which conduct the signal flow from the input
(e.g., representation error) by grouping sam-
stage to the output stage and then back to the
ples hierarchically or by iteratively reassign-
input stage of that system.
ing samples to clusters. The K-means algo-
rithmisanexampleofthelatter. Inthecaseof
2-D measurements, cluster analysis becomes
closing a basic morphological operation.
a method of image segmentation.
Given a structuring element B, the closing
by B is the composition of the dilation by B
followed by the erosion by B; it transforms clustering (1) any algorithm that creates
X into X • B = (X ⊕ B) B. The closing themajorclustersfromagivensetofpatterns.
by B is what one calls an algebraic closing; (2) a method of unsupervised learning that
this means that: (a) it is a morphological aims to discover useful structure in unlabeled
filter; (b) it is extensive, in other words it can data by grouping similar patterns.

c
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