Results 201 to 210 of about 7,268 (236)
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Application of polynomial chaos in stability and control
Automatica, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Franz S. Hover, Michael S. Triantafyllou
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Time-dependent generalized polynomial chaos
Journal of Computational Physics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marc I. Gerritsma +3 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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On stochastic LQR design and polynomial chaos
2008 American Control Conference, 2008In this paper we develop a novel theoretical framework for linear quadratic regulator design for linear systems with probabilistic uncertainty in the parameters. The framework is built on the generalized polynomial chaos theory, which can handle Gaussian, uniform, beta and gamma distributions.
James Fisher, Raktim Bhattacharya
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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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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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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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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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Multivariate Polynomial Chaos Expansions with Dependent Variables
SIAM Journal on Scientific Computing, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jonathan Feinberg +2 more
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On the accuracy of the polynomial chaos approximation
Probabilistic Engineering Mechanics, 2004Polynomial chaos representations for non-Gaussian random variables and stochastic processes are infinite series of Hermite polynomials of standard Gaussian random variables with deterministic coefficients. Finite truncations of these series are referred to as polynomial chaos (PC) approximations.
R.V. Field, M. Grigoriu
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