Abstract: In the last few years, three multivariate spectral
analysis techniques namely, Principal Component Analysis (PCA),
Independent Component Analysis (ICA) and Non-negative Matrix
Factorization (NMF) have emerged as effective tools for oscillation
detection and isolation. While the first method is used in determining
the number of oscillatory sources, the latter two methods
are used to identify source signatures by formulating the detection
problem as a source identification problem in the spectral domain.
In this paper, we present a critical drawback of the underlying linear
(mixing) model which strongly limits the ability of the associated
source separation methods to determine the number of sources
and/or identify the physical source signatures. It is shown that the
assumed mixing model is only valid if each unit of the process gives
equal weighting (all-pass filter) to all oscillatory components in its
inputs. This is in contrast to the fact that each unit, in general, acts
as a filter with non-uniform frequency response. Thus, the model
can only facilitate correct identification of a source with a single
frequency component, which is again unrealistic. To overcome
this deficiency, an iterative post-processing algorithm that correctly
identifies the physical source(s) is developed. An additional issue
with the existing methods is that they lack a procedure to pre-screen
non-oscillatory/noisy measurements which obscure the identification
of oscillatory sources. In this regard, a pre-screening procedure
is prescribed based on the notion of sparseness index to eliminate
the noisy and non-oscillatory measurements from the data set used
for analysis.
Abstract: In the past decade, because of wide applications of
hybrid systems, many researchers have considered modeling and
control of these systems. Since switching systems constitute an
important class of hybrid systems, in this paper a method for optimal
control of linear switching systems is described. The method is also
applied on the two-tank system which is a much appropriate system
to analyze different modeling and control techniques of hybrid
systems. Simulation results show that, in this method, the goals of
control and also problem constraints can be satisfied by an
appropriate selection of cost function.
Abstract: This paper investigates the inverse problem of determining
the unknown time-dependent leading coefficient in the parabolic
equation using the usual conditions of the direct problem and an additional
condition. An algorithm is developed for solving numerically
the inverse problem using the technique of space decomposition in a
reproducing kernel space. The leading coefficients can be solved by a
lower triangular linear system. Numerical experiments are presented
to show the efficiency of the proposed methods.