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Polychaos.jl : a Julia package for polynomial chaos in systems and control
Publikationstyp
Conference Paper
Date Issued
2020-01-01
Sprache
English
Author(s)
Journal
Volume
53
Issue
2
Start Page
7210
End Page
7216
Citation
IFAC-PapersOnLine 53 (2): 7210-7216
Contribution to Conference
Publisher DOI
Scopus ID
Publisher
IFAC
Polynomial chaos expansion (pce) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, pce allows for a unifying mathematical framework to study systems under arbitrary uncertainties of finite variance; we introduce this problem as a so-called mapping under uncertainty. For practical pce-based applications we require orthogonal polynomials relative to given probability densities, and their quadrature rules. With PolyChaos.jl we provide a Julia software package that delivers the desired functionality: given a probability density function, PolyChaos.jl offers several numerical routines to construct the respective orthogonal polynomials, and the quadrature rules together with tensorized scalar products. PolyChaos.jl is the first pce-related software written in Julia, a scientific programming language that combines the readability of scripted languages with the speed of compiled languages. We provide illustrating numerical examples that show both pce and PolyChaos.jl in action.
Subjects
Julia
Polynomial chaos expansion
Stochastic optimal control
Uncertainties
DDC Class
004: Computer Sciences
510: Mathematics