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＜電子ブック＞
Optimal Control of PDEs under Uncertainty : An Introduction with Application to Optimal Shape Design of Structures / by Jesús Martínez-Frutos, Francisco Periago Esparza
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
本文言語	英語
大きさ	XIX, 123 p. 45 illus., 37 illus. in color : online resource
著者標目	*Martínez-Frutos, Jesús author Periago Esparza, Francisco author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Multibody systems LCSH:Vibration LCSH:Mechanics, Applied LCSH:Solids LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Probabilities FREE:Differential Equations FREE:Mathematical and Computational Engineering Applications FREE:Multibody Systems and Mechanical Vibrations FREE:Solid Mechanics FREE:Calculus of Variations and Optimization FREE:Probability Theory
一般注記	1 Introduction -- 2 Mathematical Preliminaires -- 3 Mathematical Analysis of Optimal Control Problems Under Uncertainty -- 4 Numerical Resolution of Robust Optimal Control Problems -- 5 Numerical Resolution of Risk Averse Optimal Control Problems -- 6 Structural Optimization Under Uncertainty -- 7 Miscellaneous Topics and Open Problems This book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to offer graduate students and researchers a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk-averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition focusses on the entire path, starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples are analysed in detail throughout the book. Computer codes, written in MatLab, are provided for all these examples. This book isadressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations HTTP:URL=https://doi.org/10.1007/978-3-319-98210-6

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