208,540 research outputs found
Approximation with Random Bases: Pro et Contra
In this work we discuss the problem of selecting suitable approximators from
families of parameterized elementary functions that are known to be dense in a
Hilbert space of functions. We consider and analyze published procedures, both
randomized and deterministic, for selecting elements from these families that
have been shown to ensure the rate of convergence in norm of order
, where is the number of elements. We show that both randomized and
deterministic procedures are successful if additional information about the
families of functions to be approximated is provided. In the absence of such
additional information one may observe exponential growth of the number of
terms needed to approximate the function and/or extreme sensitivity of the
outcome of the approximation to parameters. Implications of our analysis for
applications of neural networks in modeling and control are illustrated with
examples.Comment: arXiv admin note: text overlap with arXiv:0905.067
PASSATA - Object oriented numerical simulation software for adaptive optics
We present the last version of the PyrAmid Simulator Software for Adaptive
opTics Arcetri (PASSATA), an IDL and CUDA based object oriented software
developed in the Adaptive Optics group of the Arcetri observatory for
Monte-Carlo end-to-end adaptive optics simulations. The original aim of this
software was to evaluate the performance of a single conjugate adaptive optics
system for ground based telescope with a pyramid wavefront sensor. After some
years of development, the current version of PASSATA is able to simulate
several adaptive optics systems: single conjugate, multi conjugate and ground
layer, with Shack Hartmann and Pyramid wavefront sensors. It can simulate from
8m to 40m class telescopes, with diffraction limited and resolved sources at
finite or infinite distance from the pupil. The main advantages of this
software are the versatility given by the object oriented approach and the
speed given by the CUDA implementation of the most computational demanding
routines. We describe the software with its last developments and present some
examples of application.Comment: 9 pages, 2 figures, 3 tables. SPIE conference Astronomical Telescopes
and Instrumentation, 26 June - 01 July 2016, Edinburgh, Scotland, United
Kingdo
A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure
A new unified modelling framework based on the superposition of additive submodels, functional components, and
wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented
using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown
analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear
autoregressive with exogenous inputs) model for representing dynamic inputâoutput systems. By expanding each functional
component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and
multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters
problem, which can be solved using least-squares type methods. An efficient model structure determination
approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization
of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is
employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to
as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to
represent high-order and high dimensional non-linear systems
The Harmonic Analysis of Kernel Functions
Kernel-based methods have been recently introduced for linear system
identification as an alternative to parametric prediction error methods.
Adopting the Bayesian perspective, the impulse response is modeled as a
non-stationary Gaussian process with zero mean and with a certain kernel (i.e.
covariance) function. Choosing the kernel is one of the most challenging and
important issues. In the present paper we introduce the harmonic analysis of
this non-stationary process, and argue that this is an important tool which
helps in designing such kernel. Furthermore, this analysis suggests also an
effective way to approximate the kernel, which allows to reduce the
computational burden of the identification procedure
Modelica - A Language for Physical System Modeling, Visualization and Interaction
Modelica is an object-oriented language for modeling of large, complex and heterogeneous physical systems. It is suited for multi-domain modeling, for example for modeling of mechatronics including cars, aircrafts and industrial robots which typically consist of mechanical, electrical and hydraulic subsystems as well as control systems. General equations are used for modeling of the physical phenomena, No particular variable needs to be solved for manually. A Modelica tool will have enough information to do that automatically. The language has been designed to allow tools to generate efficient code automatically. The modeling effort is thus reduced considerably since model components can be reused and tedious and error-prone manual manipulations are not needed. The principles of object-oriented modeling and the details of the Modelica language as well as several examples are presented
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