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Indirect Measurements Via Polynomial Chaos Observer
Proceedings of the 2006 IEEE International Workshop on Advanced Methods for Uncertainty Estimation in Measurement (AMUEM 2006), 2006This paper proposes an innovative approach to the design of algorithms for indirect measurements based on a polynomial chaos observer (PCO). A PCO allows the introduction and management of uncertainty in the process. The structure of this algorithm is based on the standard closed-loop structure of an observer originally introduced by Luenberger.
Anton H. C. Smith +2 more
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2014
In this chapter we review methods for formulating partial differential equations based on the random field representations outlined in Chap. 2 These include the stochastic Galerkin method, which is the predominant choice in this book, as well as other methods that frequently occur in the literature, e.g., stochastic collocation methods and spectral ...
Mass Per Pettersson +2 more
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In this chapter we review methods for formulating partial differential equations based on the random field representations outlined in Chap. 2 These include the stochastic Galerkin method, which is the predominant choice in this book, as well as other methods that frequently occur in the literature, e.g., stochastic collocation methods and spectral ...
Mass Per Pettersson +2 more
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2014
We show that given any μ > 1, an equilibrium x of a dynamic system $$\displaystyle{ x_{n+1} = f(x_{n}) }$$ (1) can be robustly stabilized by a nonlinear control $$\displaystyle{ u = -\sum _{j=1}^{N-1}\varepsilon _{ j}\left (f\left (x_{n-j+1}\right ) - f\left (x_{n-j}\right )\right ),\,\vert \varepsilon _{j}\vert < 1,\;j = 1,\ldots,N - 1, }
Dmitrishin, Dmitriy +2 more
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We show that given any μ > 1, an equilibrium x of a dynamic system $$\displaystyle{ x_{n+1} = f(x_{n}) }$$ (1) can be robustly stabilized by a nonlinear control $$\displaystyle{ u = -\sum _{j=1}^{N-1}\varepsilon _{ j}\left (f\left (x_{n-j+1}\right ) - f\left (x_{n-j}\right )\right ),\,\vert \varepsilon _{j}\vert < 1,\;j = 1,\ldots,N - 1, }
Dmitrishin, Dmitriy +2 more
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2017
Separation of variables is a powerful idea in the study of partial differential equations, and the polynomial chaos method is a particular implementation of this idea for stochastic equations. While the elementary outcome ω is typically never mentioned explicitly in the notation of random objects, it is a variable that can potentially be separated from
Sergey V. Lototsky, Boris L. Rozovsky
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Separation of variables is a powerful idea in the study of partial differential equations, and the polynomial chaos method is a particular implementation of this idea for stochastic equations. While the elementary outcome ω is typically never mentioned explicitly in the notation of random objects, it is a variable that can potentially be separated from
Sergey V. Lototsky, Boris L. Rozovsky
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Time-dependent generalized polynomial chaos
Journal of Computational Physics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gerritsma, Marc +3 more
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Multivariate Polynomial Chaos Expansions with Dependent Variables
SIAM Journal on Scientific Computing, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feinberg, Jonathan +2 more
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ROBUST CHAOS IN POLYNOMIAL UNIMODAL MAPS
International Journal of Bifurcation and Chaos, 2004Simple polynomial unimodal maps which show robust chaos, that is, a unique chaotic attractor and no periodic windows in their bifurcation diagrams, are constructed. Their invariant distributions and Lyapunov exponents are examined.
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A Polynomial Chaos Approach to Measurement Uncertainty
IEEE Transactions on Instrumentation and Measurement, 2005Measurement uncertainty is traditionally represented in the form of expanded uncertainty as defined through the Guide to the Expression of Uncertainty in Measurement (GUM). The International Organization for Standardization GUM represents uncertainty through confidence intervals based on the variances and means derived from probability density ...
T. Lovett, F. Ponci, A. Monti
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Stochastic Estimation via Polynomial Chaos
2015Abstract : This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic processes. As originally developed by Norbert Weiner, a polynomial chaos represents key properties of a stochastic process through the application of finite series of orthogonal polynomials.
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Real polynomial chaos and absolute continuity
Probability Theory and Related Fields, 1988Under very general conditions, we prove that the members of a so-called real polynomial chaos have absolutely continuous probability distributions.
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