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Structure‐exploiting polynomial chaos for uncertain optimal control problems with sparse derivative generation
Author(s) -
Bergner Lilli,
Kirches Christian
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710327
Subject(s) - polynomial chaos , parametric statistics , nonlinear system , computer science , mathematical optimization , polynomial , reuse , projection (relational algebra) , sensitivity (control systems) , algorithm , mathematics , monte carlo method , engineering , mathematical analysis , statistics , physics , quantum mechanics , electronic engineering , waste management
We present advances in structure‐exploiting non‐intrusive polynomial chaos methods for the numerical solution of nonlinear optimal control problems with parametric uncertainties. In particular, we make use of the special structure induced by the spectral projection to reuse model derivatives and exploit sparsity information leading to a fast automatic sensitivity generation. This greatly reduces the computational effort of Newton‐type methods for the solution of the resulting high‐dimensional surrogate problem. The results are complemented by a complexity comparison and a numerical case study. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)