40,847 research outputs found
On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems
This paper is a comprehensive study of a long observed phenomenon of increase
in the stability margin and so the rate of convergence of a class of linear
systems due to time delay. We use Lambert W function to determine (a) in what
systems the delay can lead to increase in the rate of convergence, (b) the
exact range of time delay for which the rate of convergence is greater than
that of the delay free system, and (c) an estimate on the value of the delay
that leads to the maximum rate of convergence. For the special case when the
system matrix eigenvalues are all negative real numbers, we expand our results
to show that the rate of convergence in the presence of delay depends only on
the eigenvalues with minimum and maximum real parts. Moreover, we determine the
exact value of the maximum rate of convergence and the corresponding maximizing
time delay. We demonstrate our results through a numerical example on the
practical application in accelerating an agreement algorithm for
networked~systems by use of a delayed feedback
Some Special Cases in the Stability Analysis of Multi-Dimensional Time-Delay Systems Using The Matrix Lambert W function
This paper revisits a recently developed methodology based on the matrix
Lambert W function for the stability analysis of linear time invariant, time
delay systems. By studying a particular, yet common, second order system, we
show that in general there is no one to one correspondence between the branches
of the matrix Lambert W function and the characteristic roots of the system.
Furthermore, it is shown that under mild conditions only two branches suffice
to find the complete spectrum of the system, and that the principal branch can
be used to find several roots, and not the dominant root only, as stated in
previous works. The results are first presented analytically, and then verified
by numerical experiments
Sensitivity of Markov chains for wireless protocols
Network communication protocols such as the IEEE 802.11 wireless protocol are currently best modelled as Markov chains. In these situations we have some protocol parameters , and a transition matrix from which we can compute the steady state (equilibrium) distribution and hence final desired quantities , which might be for example the throughput of the protocol. Typically the chain will have thousands of states, and a particular example of interest is the Bianchi chain defined later. Generally we want to optimise , perhaps subject to some constraints that also depend on the Markov chain. To do this efficiently we need the gradient of with respect to , and therefore need the gradient of and other properties of the chain with respect to . The matrix formulas available for this involve the so-called fundamental matrix, but are there approximate gradients available which are faster and still sufficiently accurate? In some cases BT would like to do the whole calculation in computer algebra, and get a series expansion of the equilibrium with respect to a parameter in . In addition to the steady state , the same questions arise for the mixing time and the mean hitting times. Two qualitative features that were brought to the Study Group’s attention were:
* the transition matrix is large, but sparse.
* the systems of linear equations to be solved are generally singular and need some additional normalisation condition, such as is provided by using the fundamental matrix.
We also note a third highly important property regarding applications of numerical linear algebra:
* the transition matrix is asymmetric.
A realistic dimension for the matrix in the Bianchi model described below is 8064Ă—8064, but on average there are only a few nonzero entries per column. Merely storing such a large matrix in dense form would require nearly 0.5GBytes using 64-bit floating point numbers, and computing its LU factorisation takes around 80 seconds on a modern microprocessor. It is thus highly desirable to employ specialised algorithms for sparse matrices. These algorithms are generally divided between those only applicable to symmetric matrices, the most prominent being the conjugate-gradient (CG) algorithm for solving linear equations, and those applicable to general matrices. A similar division is present in the literature on numerical eigenvalue problems
High Dimensional Classification with combined Adaptive Sparse PLS and Logistic Regression
Motivation: The high dimensionality of genomic data calls for the development
of specific classification methodologies, especially to prevent over-optimistic
predictions. This challenge can be tackled by compression and variable
selection, which combined constitute a powerful framework for classification,
as well as data visualization and interpretation. However, current proposed
combinations lead to instable and non convergent methods due to inappropriate
computational frameworks. We hereby propose a stable and convergent approach
for classification in high dimensional based on sparse Partial Least Squares
(sparse PLS). Results: We start by proposing a new solution for the sparse PLS
problem that is based on proximal operators for the case of univariate
responses. Then we develop an adaptive version of the sparse PLS for
classification, which combines iterative optimization of logistic regression
and sparse PLS to ensure convergence and stability. Our results are confirmed
on synthetic and experimental data. In particular we show how crucial
convergence and stability can be when cross-validation is involved for
calibration purposes. Using gene expression data we explore the prediction of
breast cancer relapse. We also propose a multicategorial version of our method
on the prediction of cell-types based on single-cell expression data.
Availability: Our approach is implemented in the plsgenomics R-package.Comment: 9 pages, 3 figures, 4 tables + Supplementary Materials 8 pages, 3
figures, 10 table
PV panel modeling and identification
In this chapter, the modelling techniques of PV panels from I-V characteristics
are discussed. At the beginning, a necessary review on the various methods are presented,
where difficulties in mathematics, drawbacks in accuracy, and challenges in
implementation are highlighted. Next, a novel approach based on linear system identification
is demonstrated in detail. Other than the prevailing methods of using approximation
(analytical methods), iterative searching (classical optimization), or soft
computing (artificial intelligence), the proposed method regards the PV diode model
as the equivalent output of a dynamic system, so the diode model parameters can be
linked to the transfer function coefficients of the same dynamic system. In this way,
the problem of solving PV model parameters is equivalently converted to system identification
in control theory, which can be perfectly solved by a simple integral-based
linear least square method. Graphical meanings of the proposed method are illustrated
to help readers understand the underlying principles. As compared to other methods,
the proposed one has the following benefits: 1) unique solution; 2) no iterative or
global searching; 3) easy to implement (linear least square); 4) accuracy; 5) extendable
to multi-diode models. The effectiveness of the proposed method has been verified by
indoor and outdoor PV module testing results. In addition, possible applications of
the proposed method are discussed like online PV monitoring and diagnostics, noncontact
measurement of POA irradiance and cell temperature, fast model identification
for satellite PV panels, and etc
On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay
This paper studies the robustness of a dynamic average consensus algorithm to
communication delay over strongly connected and weight-balanced (SCWB)
digraphs. Under delay-free communication, the algorithm of interest achieves a
practical asymptotic tracking of the dynamic average of the time-varying
agents' reference signals. For this algorithm, in both its continuous-time and
discrete-time implementations, we characterize the admissible communication
delay range and study the effect of the delay on the rate of convergence and
the tracking error bound. Our study also includes establishing a relationship
between the admissible delay bound and the maximum degree of the SCWB digraphs.
We also show that for delays in the admissible bound, for static signals the
algorithms achieve perfect tracking. Moreover, when the interaction topology is
a connected undirected graph, we show that the discrete-time implementation is
guaranteed to tolerate at least one step delay. Simulations demonstrate our
results
- …