27,751 research outputs found
Computing an Optimal Control Policy for an Energy Storage
We introduce StoDynProg, a small library created to solve Optimal Control
problems arising in the management of Renewable Power Sources, in particular
when coupled with an Energy Storage System. The library implements generic
Stochastic Dynamic Programming (SDP) numerical methods which can solve a large
class of Dynamic Optimization problems. We demonstrate the library capabilities
with a prototype problem: smoothing the power of an Ocean Wave Energy
Converter. First we use time series analysis to derive a stochastic Markovian
model of this system since it is required by Dynamic Programming. Then, we
briefly describe the "policy iteration" algorithm we have implemented and the
numerical tools being used. We show how the API design of the library is
generic enough to address Dynamic Optimization problems outside the field of
Energy Management. Finally, we solve the power smoothing problem and compare
the optimal control with a simpler heuristic control.Comment: Part of the Proceedings of the 6th European Conference on Python in
Science (EuroSciPy 2013), Pierre de Buyl and Nelle Varoquaux editors, (2014
Recommended from our members
Review of Unbiased FIR Filters, Smoothers, and Predictors for Polynomial Signals
Extracting an estimate of a slowly varying signal corrupted by noise is a common task. Examples can be found in industrial, scientific and biomedical instrumentation. Depending on the nature of the application the signal estimate is allowed to be a delayed estimate of the original signal or, in the other extreme, no delay is tolerated. These cases are commonly referred to as filtering, prediction, and smoothing depending on the amount of advance or lag between the input data set and the output data set. In this review paper we provide a comprehensive set of design and analysis tools for designing unbiased FIR filters, predictors, and smoothers for slowly varying signals, i.e. signals that can be modeled by low order polynomials. Explicit expressions of parameters needed in practical implementations are given. Real life examples are provided including cases where the method is extended to signals that are piecewise slowly varying. A critical view on recursive implementations of the algorithms is provided
Fast Ensemble Smoothing
Smoothing is essential to many oceanographic, meteorological and hydrological
applications. The interval smoothing problem updates all desired states within
a time interval using all available observations. The fixed-lag smoothing
problem updates only a fixed number of states prior to the observation at
current time. The fixed-lag smoothing problem is, in general, thought to be
computationally faster than a fixed-interval smoother, and can be an
appropriate approximation for long interval-smoothing problems. In this paper,
we use an ensemble-based approach to fixed-interval and fixed-lag smoothing,
and synthesize two algorithms. The first algorithm produces a linear time
solution to the interval smoothing problem with a fixed factor, and the second
one produces a fixed-lag solution that is independent of the lag length.
Identical-twin experiments conducted with the Lorenz-95 model show that for lag
lengths approximately equal to the error doubling time, or for long intervals
the proposed methods can provide significant computational savings. These
results suggest that ensemble methods yield both fixed-interval and fixed-lag
smoothing solutions that cost little additional effort over filtering and model
propagation, in the sense that in practical ensemble application the additional
increment is a small fraction of either filtering or model propagation costs.
We also show that fixed-interval smoothing can perform as fast as fixed-lag
smoothing and may be advantageous when memory is not an issue
Large-scale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications
In computer vision, many problems such as image segmentation, pixel
labelling, and scene parsing can be formulated as binary quadratic programs
(BQPs). For submodular problems, cuts based methods can be employed to
efficiently solve large-scale problems. However, general nonsubmodular problems
are significantly more challenging to solve. Finding a solution when the
problem is of large size to be of practical interest, however, typically
requires relaxation. Two standard relaxation methods are widely used for
solving general BQPs--spectral methods and semidefinite programming (SDP), each
with their own advantages and disadvantages. Spectral relaxation is simple and
easy to implement, but its bound is loose. Semidefinite relaxation has a
tighter bound, but its computational complexity is high, especially for large
scale problems. In this work, we present a new SDP formulation for BQPs, with
two desirable properties. First, it has a similar relaxation bound to
conventional SDP formulations. Second, compared with conventional SDP methods,
the new SDP formulation leads to a significantly more efficient and scalable
dual optimization approach, which has the same degree of complexity as spectral
methods. We then propose two solvers, namely, quasi-Newton and smoothing Newton
methods, for the dual problem. Both of them are significantly more efficiently
than standard interior-point methods. In practice, the smoothing Newton solver
is faster than the quasi-Newton solver for dense or medium-sized problems,
while the quasi-Newton solver is preferable for large sparse/structured
problems. Our experiments on a few computer vision applications including
clustering, image segmentation, co-segmentation and registration show the
potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern
Analysis and Machine Intelligenc
PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers
The interpretation of the intensity and polarization of the spectral line
radiation produced in the atmosphere of the Sun and of other stars requires
solving a radiative transfer problem that can be very complex, especially when
the main interest lies in modeling the spectral line polarization produced by
scattering processes and the Hanle and Zeeman effects. One of the difficulties
is that the plasma of a stellar atmosphere can be highly inhomogeneous and
dynamic, which implies the need to solve the non-equilibrium problem of the
generation and transfer of polarized radiation in realistic three-dimensional
(3D) stellar atmospheric models. Here we present PORTA, an efficient multilevel
radiative transfer code we have developed for the simulation of the spectral
line polarization caused by scattering processes and the Hanle and Zeeman
effects in 3D models of stellar atmospheres. The numerical method of solution
is based on the non-linear multigrid iterative method and on a novel
short-characteristics formal solver of the Stokes-vector transfer equation
which uses monotonic B\'ezier interpolation. Therefore, with PORTA the
computing time needed to obtain at each spatial grid point the self-consistent
values of the atomic density matrix (which quantifies the excitation state of
the atomic system) scales linearly with the total number of grid points.
Another crucial feature of PORTA is its parallelization strategy, which allows
us to speed up the numerical solution of complicated 3D problems by several
orders of magnitude with respect to sequential radiative transfer approaches,
given its excellent linear scaling with the number of available processors. The
PORTA code can also be conveniently applied to solve the simpler 3D radiative
transfer problem of unpolarized radiation in multilevel systems.Comment: 15 pages, 15 figures, to appear in Astronomy and Astrophysic
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