文章基本信息

标题：PolyChaos.jl — A Julia Package for Polynomial Chaos in Systems and Control
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作者：Tillmann Mühlpfordt ; Frederik Zahn ; Veit Hagenmeyer 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2020
卷号：53
期号：2
页码：7210-7216
DOI：10.1016/j.ifacol.2020.12.552
语种：English
出版社：Elsevier
摘要：AbstractPolynomial 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. WithPolyChaos.jlwe provide a Julia software package that delivers the desired functionality: given a probability density function,PolyChaos.jloffers several numerical routines to construct the respective orthogonal polynomials, and the quadrature rules together with tensorized scalar products.PolyChaos.jlis 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 andPolyChaos.jlin action.
关键词：Keywordspolynomial chaos expansionuncertaintiesstochastic optimal controlJulia