25,414 research outputs found
Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces
© 2007 EUCA.A novel online-computation approach to optimal control of nonlinear, noise-affected systems with continuous state and control spaces is presented. In the proposed algorithm, system noise is explicitly incorporated into the control decision. This leads to superior results compared to state-of-the-art nonlinear controllers that neglect this influence. The solution of an optimal nonlinear controller for a corresponding deterministic system is employed to find a meaningful state space restriction. This restriction is obtained by means of approximate state prediction using the noisy system equation. Within this constrained state space, an optimal closed-loop solution for a finite decision-making horizon (prediction horizon) is determined within an adaptively restricted optimization space. Interleaving stochastic dynamic programming and value function approximation yields a solution to the considered optimal control problem. The enhanced performance of the proposed discrete-time controller is illustrated by means of a scalar example system. Nonlinear model predictive control is applied to address approximate treatment of infinite-horizon problems by the finite-horizon controller
Biorthogonal partners and applications
Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
Fractional biorthogonal partners in channel equalization and signal interpolation
The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners
Nonparametric likelihood based estimation of linear filters for point processes
We consider models for multivariate point processes where the intensity is
given nonparametrically in terms of functions in a reproducing kernel Hilbert
space. The likelihood function involves a time integral and is consequently not
given in terms of a finite number of kernel evaluations. The main result is a
representation of the gradient of the log-likelihood, which we use to derive
computable approximations of the log-likelihood and the gradient by time
discretization. These approximations are then used to minimize the approximate
penalized log-likelihood. For time and memory efficiency the implementation
relies crucially on the use of sparse matrices. As an illustration we consider
neuron network modeling, and we use this example to investigate how the
computational costs of the approximations depend on the resolution of the time
discretization. The implementation is available in the R package ppstat.Comment: 10 pages, 3 figure
Smooth quasi-developable surfaces bounded by smooth curves
Computing a quasi-developable strip surface bounded by design curves finds
wide industrial applications. Existing methods compute discrete surfaces
composed of developable lines connecting sampling points on input curves which
are not adequate for generating smooth quasi-developable surfaces. We propose
the first method which is capable of exploring the full solution space of
continuous input curves to compute a smooth quasi-developable ruled surface
with as large developability as possible. The resulting surface is exactly
bounded by the input smooth curves and is guaranteed to have no
self-intersections. The main contribution is a variational approach to compute
a continuous mapping of parameters of input curves by minimizing a function
evaluating surface developability. Moreover, we also present an algorithm to
represent a resulting surface as a B-spline surface when input curves are
B-spline curves.Comment: 18 page
On causal extrapolation of sequences with applications to forecasting
The paper suggests a method of extrapolation of notion of one-sided
semi-infinite sequences representing traces of two-sided band-limited
sequences; this features ensure uniqueness of this extrapolation and
possibility to use this for forecasting. This lead to a forecasting method for
more general sequences without this feature based on minimization of the mean
square error between the observed path and a predicable sequence. These
procedure involves calculation of this predictable path; the procedure can be
interpreted as causal smoothing. The corresponding smoothed sequences allow
unique extrapolations to future times that can be interpreted as optimal
forecasts.Comment: arXiv admin note: substantial text overlap with arXiv:1111.670
A new code for orbit analysis and Schwarzschild modelling of triaxial stellar systems
We review the methods used to study the orbital structure and chaotic
properties of various galactic models and to construct self-consistent
equilibrium solutions by Schwarzschild's orbit superposition technique. These
methods are implemented in a new publicly available software tool, SMILE, which
is intended to be a convenient and interactive instrument for studying a
variety of 2D and 3D models, including arbitrary potentials represented by a
basis-set expansion, a spherical-harmonic expansion with coefficients being
smooth functions of radius (splines), or a set of fixed point masses. We also
propose two new variants of Schwarzschild modelling, in which the density of
each orbit is represented by the coefficients of the basis-set or spline
spherical-harmonic expansion, and the orbit weights are assigned in such a way
as to reproduce the coefficients of the underlying density model. We explore
the accuracy of these general-purpose potential expansions and show that they
may be efficiently used to approximate a wide range of analytic density models
and serve as smooth representations of discrete particle sets (e.g. snapshots
from an N-body simulation), for instance, for the purpose of orbit analysis of
the snapshot. For the variants of Schwarzschild modelling, we use two test
cases - a triaxial Dehnen model containing a central black hole, and a model
re-created from an N-body snapshot obtained by a cold collapse. These tests
demonstrate that all modelling approaches are capable of creating equilibrium
models.Comment: MNRAS, 24 pages, 18 figures. Software is available at
http://td.lpi.ru/~eugvas/smile
Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: explicit time-stepping and efficient mass matrix inversion
We present a class of spline finite element methods for time-domain wave
propagation which are particularly amenable to explicit time-stepping. The
proposed methods utilize a discontinuous Galerkin discretization to enforce
continuity of the solution field across geometric patches in a multi-patch
setting, which yields a mass matrix with convenient block diagonal structure.
Over each patch, we show how to accurately and efficiently invert mass matrices
in the presence of curved geometries by using a weight-adjusted approximation
of the mass matrix inverse. This approximation restores a tensor product
structure while retaining provable high order accuracy and semi-discrete energy
stability. We also estimate the maximum stable timestep for spline-based finite
elements and show that the use of spline spaces result in less stringent CFL
restrictions than equivalent piecewise continuous or discontinuous finite
element spaces. Finally, we explore the use of optimal knot vectors based on L2
n-widths. We show how the use of optimal knot vectors can improve both
approximation properties and the maximum stable timestep, and present a simple
heuristic method for approximating optimal knot positions. Numerical
experiments confirm the accuracy and stability of the proposed methods
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