5,163 research outputs found
Nonlinear Model Predictive Control Considering Stochastic and Systematic Uncertainties with Sets of Densities
In Model Predictive Control, the quality of control is highly dependent upon the model of the system under control. Therefore, a precise deterministic model is desirable. However, in real-world applications, modeling accuracy is typically limited and systems are generally affected by disturbances. Hence, it is important to systematically consider these uncertainties and to model them correctly. In this paper, we present a novel Nonlinear Model Predictive Control method for systems affected by two different types of perturbations that are modeled as being either stochastic or unknown but bounded quantities. We derive a formal generalization of the Nonlinear Model Predictive Control principle for considering both types of uncertainties simultaneously, which is achieved by using sets of probability densities. In doing so, a more robust and reliable control is obtained. The capabilities and benefits of our approach are demonstrated in real-world experiments with miniature walking robots
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
Wind Energy: Forecasting Challenges for its Operational Management
Renewable energy sources, especially wind energy, are to play a larger role
in providing electricity to industrial and domestic consumers. This is already
the case today for a number of European countries, closely followed by the US
and high growth countries, for example, Brazil, India and China. There exist a
number of technological, environmental and political challenges linked to
supplementing existing electricity generation capacities with wind energy.
Here, mathematicians and statisticians could make a substantial contribution at
the interface of meteorology and decision-making, in connection with the
generation of forecasts tailored to the various operational decision problems
involved. Indeed, while wind energy may be seen as an environmentally friendly
source of energy, full benefits from its usage can only be obtained if one is
able to accommodate its variability and limited predictability. Based on a
short presentation of its physical basics, the importance of considering wind
power generation as a stochastic process is motivated. After describing
representative operational decision-making problems for both market
participants and system operators, it is underlined that forecasts should be
issued in a probabilistic framework. Even though, eventually, the forecaster
may only communicate single-valued predictions. The existing approaches to wind
power forecasting are subsequently described, with focus on single-valued
predictions, predictive marginal densities and space-time trajectories.
Upcoming challenges related to generating improved and new types of forecasts,
as well as their verification and value to forecast users, are finally
discussed.Comment: Published in at http://dx.doi.org/10.1214/13-STS445 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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Dual state-parameter estimation of hydrological models using ensemble Kalman filter
Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state-parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model. © 2004 Elsevier Ltd. All rights reserved
Type Ia Supernova Light Curve Inference: Hierarchical Bayesian Analysis in the Near Infrared
We present a comprehensive statistical analysis of the properties of Type Ia
SN light curves in the near infrared using recent data from PAIRITEL and the
literature. We construct a hierarchical Bayesian framework, incorporating
several uncertainties including photometric error, peculiar velocities, dust
extinction and intrinsic variations, for coherent statistical inference. SN Ia
light curve inferences are drawn from the global posterior probability of
parameters describing both individual supernovae and the population conditioned
on the entire SN Ia NIR dataset. The logical structure of the hierarchical
model is represented by a directed acyclic graph. Fully Bayesian analysis of
the model and data is enabled by an efficient MCMC algorithm exploiting the
conditional structure using Gibbs sampling. We apply this framework to the
JHK_s SN Ia light curve data. A new light curve model captures the observed
J-band light curve shape variations. The intrinsic variances in peak absolute
magnitudes are: sigma(M_J) = 0.17 +/- 0.03, sigma(M_H) = 0.11 +/- 0.03, and
sigma(M_Ks) = 0.19 +/- 0.04. We describe the first quantitative evidence for
correlations between the NIR absolute magnitudes and J-band light curve shapes,
and demonstrate their utility for distance estimation. The average residual in
the Hubble diagram for the training set SN at cz > 2000 km/s is 0.10 mag. The
new application of bootstrap cross-validation to SN Ia light curve inference
tests the sensitivity of the model fit to the finite sample and estimates the
prediction error at 0.15 mag. These results demonstrate that SN Ia NIR light
curves are as effective as optical light curves, and, because they are less
vulnerable to dust absorption, they have great potential as precise and
accurate cosmological distance indicators.Comment: 24 pages, 15 figures, 4 tables. Accepted for publication in ApJ.
Corrected typo, added references, minor edit
Physics-Based Probabilistic Motion Compensation of Elastically Deformable Objects
A predictive tracking approach and a novel method for visual motion compensation are introduced, which accurately reconstruct and compensate the deformation of the elastic object, even in the case of complete measurement information loss. The core of the methods involves a probabilistic physical model of the object, from which all other mathematical models are systematically derived. Due to flexible adaptation of the models, the balance between their complexity and their accuracy is achieved
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