89,750 research outputs found
A fast stroboscopic spectral method for rotating systems in numerical relativity
We present a numerical technique for solving evolution equations, as the wave
equation, in the description of rotating astrophysical compact objects in
comoving coordinates, which avoids the problems associated with the light
cylinder. The technique implements a fast spectral matching between two domains
in relative rotation: an inner spherical domain, comoving with the sources and
lying strictly inside the light cylinder, and an outer inertial spherical
shell. Even though the emphasis is placed on spectral techniques, the matching
is independent of the specific manner in which equations are solved inside each
domain, and can be adapted to different schemes. We illustrate the strategy
with some simple but representative examples.Comment: 16 pages, 15 figure
Nested Sampling with Constrained Hamiltonian Monte Carlo
Nested sampling is a powerful approach to Bayesian inference ultimately
limited by the computationally demanding task of sampling from a heavily
constrained probability distribution. An effective algorithm in its own right,
Hamiltonian Monte Carlo is readily adapted to efficiently sample from any
smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte
Carlo, I introduce a general implementation of the nested sampling algorithm.Comment: 15 pages, 4 figure
SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget
In the context of industrial engineering, it is important to integrate
efficient computational optimization methods in the product development
process. Some of the most challenging simulation-based engineering design
optimization problems are characterized by: a large number of design variables,
the absence of analytical gradients, highly non-linear objectives and a limited
function evaluation budget. Although a huge variety of different optimization
algorithms is available, the development and selection of efficient algorithms
for problems with these industrial relevant characteristics, remains a
challenge. In this communication, a hybrid variant of Differential Evolution
(DE) is introduced which combines aspects of Stochastic Quasi-Gradient (SQG)
methods within the framework of DE, in order to improve optimization efficiency
on problems with the previously mentioned characteristics. The performance of
the resulting derivative-free algorithm is compared with other state-of-the-art
DE variants on 25 commonly used benchmark functions, under tight function
evaluation budget constraints of 1000 evaluations. The experimental results
indicate that the new algorithm performs excellent on the 'difficult' (high
dimensional, multi-modal, inseparable) test functions. The operations used in
the proposed mutation scheme, are computationally inexpensive, and can be
easily implemented in existing differential evolution variants or other
population-based optimization algorithms by a few lines of program code as an
non-invasive optional setting. Besides the applicability of the presented
algorithm by itself, the described concepts can serve as a useful and
interesting addition to the algorithmic operators in the frameworks of
heuristics and evolutionary optimization and computing
A Bayesian approach to the semi-analytic model of galaxy formation: methodology
We believe that a wide range of physical processes conspire to shape the
observed galaxy population but we remain unsure of their detailed interactions.
The semi-analytic model (SAM) of galaxy formation uses multi-dimensional
parameterisations of the physical processes of galaxy formation and provides a
tool to constrain these underlying physical interactions. Because of the high
dimensionality, the parametric problem of galaxy formation may be profitably
tackled with a Bayesian-inference based approach, which allows one to constrain
theory with data in a statistically rigorous way. In this paper we develop a
SAM in the framework of Bayesian inference. We show that, with a parallel
implementation of an advanced Markov-Chain Monte-Carlo algorithm, it is now
possible to rigorously sample the posterior distribution of the
high-dimensional parameter space of typical SAMs. As an example, we
characterise galaxy formation in the current CDM cosmology using the
stellar mass function of galaxies as an observational constraint. We find that
the posterior probability distribution is both topologically complex and
degenerate in some important model parameters, suggesting that thorough
explorations of the parameter space are needed to understand the models. We
also demonstrate that because of the model degeneracy, adopting a narrow prior
strongly restricts the model. Therefore, the inferences based on SAMs are
conditional to the model adopted. Using synthetic data to mimic systematic
errors in the stellar mass function, we demonstrate that an accurate
observational error model is essential to meaningful inference.Comment: revised version to match published article published in MNRA
Robust MPC of constrained nonlinear systems based on interval arithmetic
A robust MPC for constrained discrete-time nonlinear systems with additive
uncertainties is presented. The proposed controller is based on the concept of reachable sets, that
is, the sets that contain the predicted evolution of the uncertain system for all possible uncertainties.
If processes are nonlinear these sets are very difficult to compute. A conservative approximation
based on interval arithmetic is proposed for the online computation of these sets. This technique
provides good results with a computational effort only slightly greater than the one corresponding to
the nominal prediction. These sets are incorporated into the MPC formulation to achieve robust
stability. By choosing a robust positively invariant set as a terminal constraint, a robustly stabilising
controller is obtained. Stability is guaranteed in the case of suboptimality of the computed solution.
The proposed controller is applied to a continuous stirred tank reactor with an exothermic reaction.Ministerio de Ciencia y Tecnología DPI-2001-2380-03- 01Ministerio de Ciencia y Tecnología DPI-2002-4375-C02-0
Implementation of Nonlinear Model Predictive Path-Following Control for an Industrial Robot
Many robotic applications, such as milling, gluing, or high precision
measurements, require the exact following of a pre-defined geometric path. In
this paper, we investigate the real-time feasible implementation of model
predictive path-following control for an industrial robot. We consider
constrained output path following with and without reference speed assignment.
We present results from an implementation of the proposed model predictive
path-following controller on a KUKA LWR IV robot.Comment: 8 pages, 3 figures; final revised versio
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