2,209 research outputs found
Equivalence Theorems in Numerical Analysis : Integration, Differentiation and Interpolation
We show that if a numerical method is posed as a sequence of operators acting
on data and depending on a parameter, typically a measure of the size of
discretization, then consistency, convergence and stability can be related by a
Lax-Richtmyer type equivalence theorem -- a consistent method is convergent if
and only if it is stable. We define consistency as convergence on a dense
subspace and stability as discrete well-posedness. In some applications
convergence is harder to prove than consistency or stability since convergence
requires knowledge of the solution. An equivalence theorem can be useful in
such settings. We give concrete instances of equivalence theorems for
polynomial interpolation, numerical differentiation, numerical integration
using quadrature rules and Monte Carlo integration.Comment: 18 page
Data-based mechanistic modelling, forecasting, and control.
This article briefly reviews the main aspects of the generic data based mechanistic (DBM) approach to modeling stochastic dynamic systems and shown how it is being applied to the analysis, forecasting, and control of environmental and agricultural systems. The advantages of this inductive approach to modeling lie in its wide range of applicability. It can be used to model linear, nonstationary, and nonlinear stochastic systems, and its exploitation of recursive estimation means that the modeling results are useful for both online and offline applications. To demonstrate the practical utility of the various methodological tools that underpin the DBM approach, the article also outlines several typical, practical examples in the area of environmental and agricultural systems analysis, where DBM models have formed the basis for simulation model reduction, control system design, and forecastin
Investigation of Air Transportation Technology at Princeton University, 1989-1990
The Air Transportation Technology Program at Princeton University proceeded along six avenues during the past year: microburst hazards to aircraft; machine-intelligent, fault tolerant flight control; computer aided heuristics for piloted flight; stochastic robustness for flight control systems; neural networks for flight control; and computer aided control system design. These topics are briefly discussed, and an annotated bibliography of publications that appeared between January 1989 and June 1990 is given
Towards Efficient Maximum Likelihood Estimation of LPV-SS Models
How to efficiently identify multiple-input multiple-output (MIMO) linear
parameter-varying (LPV) discrete-time state-space (SS) models with affine
dependence on the scheduling variable still remains an open question, as
identification methods proposed in the literature suffer heavily from the curse
of dimensionality and/or depend on over-restrictive approximations of the
measured signal behaviors. However, obtaining an SS model of the targeted
system is crucial for many LPV control synthesis methods, as these synthesis
tools are almost exclusively formulated for the aforementioned representation
of the system dynamics. Therefore, in this paper, we tackle the problem by
combining state-of-the-art LPV input-output (IO) identification methods with an
LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step.
The resulting modular LPV-SS identification approach achieves statical
efficiency with a relatively low computational load. The method contains the
following three steps: 1) estimation of the Markov coefficient sequence of the
underlying system using correlation analysis or Bayesian impulse response
estimation, then 2) LPV-SS realization of the estimated coefficients by using a
basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate
from a maximum-likelihood point of view by a gradient-based or an
expectation-maximization optimization methodology. The effectiveness of the
full identification scheme is demonstrated by a Monte Carlo study where our
proposed method is compared to existing schemes for identifying a MIMO LPV
system
A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks
We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with no-arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1991.
Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction
Considering the competitive and strongly regulated pharmaceutical industry, mathematical
modeling and process systems engineering might be useful tools for implementing quality by
design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However,
a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification
of model candidates from a set of various model hypotheses. To identify the best experimental
design suitable for a reliable model selection and system identification is challenging for nonlinear
(bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness
for model selection problems under uncertainty, and thus translates the model selection problem
to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal
controls for improved model selection trajectories are expressed analytically with low computational
costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based
method and provide an effective robustification strategy with the point estimate method for
uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating
the carboligation of aldehydes, where we successfully derive optimal controls for improved model
selection trajectories under uncertainty
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