The Resource Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures, Jesús MartínezFrutos, Francisco Periago Esparza
Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures, Jesús MartínezFrutos, Francisco Periago Esparza
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The item Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures, Jesús MartínezFrutos, Francisco Periago Esparza represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures, Jesús MartínezFrutos, Francisco Periago Esparza represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 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 riskaverse 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 is adressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.
 Language
 eng
 Extent
 1 online resource.
 Contents

 Intro; Preface; References; Contents; About the Authors; Acronyms and Initialisms; Abstract; 1 Introduction; 1.1 Motivation; 1.2 Modelling Uncertainty in the Input Data. Illustrative Examples; 1.2.1 The LaplacePoisson Equation; 1.2.2 The Heat Equation; 1.2.3 The BernoulliEuler Beam Equation; References; 2 Mathematical Preliminaires; 2.1 Basic Definitions and Notations; 2.2 Tensor Product of Hilbert Spaces; 2.3 Numerical Approximation of Random Fields; 2.3.1 KarhunenLoève Expansion of a Random Field; 2.4 Notes and Related Software; References
 3 Mathematical Analysis of Optimal Control Problems Under Uncertainty3.1 Variational Formulation of Random PDEs; 3.1.1 The LaplacePoisson Equation Revisited I; 3.1.2 The Heat Equation Revisited I; 3.1.3 The BernoulliEuler Beam Equation Revisited I; 3.2 Existence of Optimal Controls Under Uncertainty; 3.2.1 Robust Optimal Control Problems; 3.2.2 Risk Averse Optimal Control Problems; 3.3 Differences Between Robust and RiskAverse Optimal Control; 3.4 Notes; References; 4 Numerical Resolution of Robust Optimal Control Problems
 4.1 FiniteDimensional Noise Assumption: From Random PDEs to Deterministic PDEs with a FiniteDimensional Parameter4.2 GradientBased Methods; 4.2.1 Computing Gradients of Functionals Measuring Robustness; 4.2.2 Numerical Approximation of Quantities of Interest in Robust Optimal Control Problems; 4.2.3 Numerical Experiments; 4.3 Benefits and Drawbacks of the Cost Functionals; 4.4 OneShot Methods; 4.5 Notes and Related Software; References; 5 Numerical Resolution of Risk Averse Optimal Control Problems; 5.1 An Adaptive, GradientBased, Minimization Algorithm
 5.2 Computing Gradients of Functionals Measuring Risk Aversion5.3 Numerical Approximation of Quantities of Interest in Risk Averse Optimal Control Problems; 5.3.1 An Anisotropic, Nonintrusive, Stochastic Galerkin Method; 5.3.2 Adaptive Algorithm to Select the Level of Approximation; 5.3.3 Choosing Monte Carlo Samples for Numerical Integration; 5.4 Numerical Experiments; 5.5 Notes and Related Software; References; 6 Structural Optimization Under Uncertainty; 6.1 Problem Formulation; 6.2 Existence of Optimal Shapes; 6.3 Numerical Approximation via the LevelSet Method
 6.3.1 Computing Gradients of Shape Functionals; 6.3.2 Mise en Scène of the Level Set Method; 6.4 Numerical Simulation Results; 6.5 Notes and Related Software; References; 7 Miscellaneous Topics and Open Problems; 7.1 The Heat Equation Revisited II; 7.2 The BernoulliEuler Beam Equation Revisited II; 7.3 Concluding Remarks and Some Open Problems; References; Index
 Isbn
 9783319982090
 Label
 Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures
 Title
 Optimal control of PDEs under uncertainty
 Title remainder
 an introduction with application to optimal shape design of structures
 Statement of responsibility
 Jesús MartínezFrutos, Francisco Periago Esparza
 Language
 eng
 Summary
 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 riskaverse 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 is adressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.
 Assigning source
 Provided by publisher
 Cataloging source
 N$T
 http://library.link/vocab/creatorName
 MartínezFrutos, Jesús
 Dewey number
 515.353
 Index
 index present
 LC call number
 QA374
 LC item number
 .M37 2018
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Esparza, Francisco Periago
 Series statement

 SpringerBriefs in mathematics
 BCAM SpringerBriefs
 http://library.link/vocab/subjectName
 Differential equations, Partial
 Label
 Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures, Jesús MartínezFrutos, Francisco Periago Esparza
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Intro; Preface; References; Contents; About the Authors; Acronyms and Initialisms; Abstract; 1 Introduction; 1.1 Motivation; 1.2 Modelling Uncertainty in the Input Data. Illustrative Examples; 1.2.1 The LaplacePoisson Equation; 1.2.2 The Heat Equation; 1.2.3 The BernoulliEuler Beam Equation; References; 2 Mathematical Preliminaires; 2.1 Basic Definitions and Notations; 2.2 Tensor Product of Hilbert Spaces; 2.3 Numerical Approximation of Random Fields; 2.3.1 KarhunenLoève Expansion of a Random Field; 2.4 Notes and Related Software; References
 3 Mathematical Analysis of Optimal Control Problems Under Uncertainty3.1 Variational Formulation of Random PDEs; 3.1.1 The LaplacePoisson Equation Revisited I; 3.1.2 The Heat Equation Revisited I; 3.1.3 The BernoulliEuler Beam Equation Revisited I; 3.2 Existence of Optimal Controls Under Uncertainty; 3.2.1 Robust Optimal Control Problems; 3.2.2 Risk Averse Optimal Control Problems; 3.3 Differences Between Robust and RiskAverse Optimal Control; 3.4 Notes; References; 4 Numerical Resolution of Robust Optimal Control Problems
 4.1 FiniteDimensional Noise Assumption: From Random PDEs to Deterministic PDEs with a FiniteDimensional Parameter4.2 GradientBased Methods; 4.2.1 Computing Gradients of Functionals Measuring Robustness; 4.2.2 Numerical Approximation of Quantities of Interest in Robust Optimal Control Problems; 4.2.3 Numerical Experiments; 4.3 Benefits and Drawbacks of the Cost Functionals; 4.4 OneShot Methods; 4.5 Notes and Related Software; References; 5 Numerical Resolution of Risk Averse Optimal Control Problems; 5.1 An Adaptive, GradientBased, Minimization Algorithm
 5.2 Computing Gradients of Functionals Measuring Risk Aversion5.3 Numerical Approximation of Quantities of Interest in Risk Averse Optimal Control Problems; 5.3.1 An Anisotropic, Nonintrusive, Stochastic Galerkin Method; 5.3.2 Adaptive Algorithm to Select the Level of Approximation; 5.3.3 Choosing Monte Carlo Samples for Numerical Integration; 5.4 Numerical Experiments; 5.5 Notes and Related Software; References; 6 Structural Optimization Under Uncertainty; 6.1 Problem Formulation; 6.2 Existence of Optimal Shapes; 6.3 Numerical Approximation via the LevelSet Method
 6.3.1 Computing Gradients of Shape Functionals; 6.3.2 Mise en Scène of the Level Set Method; 6.4 Numerical Simulation Results; 6.5 Notes and Related Software; References; 7 Miscellaneous Topics and Open Problems; 7.1 The Heat Equation Revisited II; 7.2 The BernoulliEuler Beam Equation Revisited II; 7.3 Concluding Remarks and Some Open Problems; References; Index
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319982090
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 on1050448291
 (OCoLC)1050448291
 Label
 Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures, Jesús MartínezFrutos, Francisco Periago Esparza
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Intro; Preface; References; Contents; About the Authors; Acronyms and Initialisms; Abstract; 1 Introduction; 1.1 Motivation; 1.2 Modelling Uncertainty in the Input Data. Illustrative Examples; 1.2.1 The LaplacePoisson Equation; 1.2.2 The Heat Equation; 1.2.3 The BernoulliEuler Beam Equation; References; 2 Mathematical Preliminaires; 2.1 Basic Definitions and Notations; 2.2 Tensor Product of Hilbert Spaces; 2.3 Numerical Approximation of Random Fields; 2.3.1 KarhunenLoève Expansion of a Random Field; 2.4 Notes and Related Software; References
 3 Mathematical Analysis of Optimal Control Problems Under Uncertainty3.1 Variational Formulation of Random PDEs; 3.1.1 The LaplacePoisson Equation Revisited I; 3.1.2 The Heat Equation Revisited I; 3.1.3 The BernoulliEuler Beam Equation Revisited I; 3.2 Existence of Optimal Controls Under Uncertainty; 3.2.1 Robust Optimal Control Problems; 3.2.2 Risk Averse Optimal Control Problems; 3.3 Differences Between Robust and RiskAverse Optimal Control; 3.4 Notes; References; 4 Numerical Resolution of Robust Optimal Control Problems
 4.1 FiniteDimensional Noise Assumption: From Random PDEs to Deterministic PDEs with a FiniteDimensional Parameter4.2 GradientBased Methods; 4.2.1 Computing Gradients of Functionals Measuring Robustness; 4.2.2 Numerical Approximation of Quantities of Interest in Robust Optimal Control Problems; 4.2.3 Numerical Experiments; 4.3 Benefits and Drawbacks of the Cost Functionals; 4.4 OneShot Methods; 4.5 Notes and Related Software; References; 5 Numerical Resolution of Risk Averse Optimal Control Problems; 5.1 An Adaptive, GradientBased, Minimization Algorithm
 5.2 Computing Gradients of Functionals Measuring Risk Aversion5.3 Numerical Approximation of Quantities of Interest in Risk Averse Optimal Control Problems; 5.3.1 An Anisotropic, Nonintrusive, Stochastic Galerkin Method; 5.3.2 Adaptive Algorithm to Select the Level of Approximation; 5.3.3 Choosing Monte Carlo Samples for Numerical Integration; 5.4 Numerical Experiments; 5.5 Notes and Related Software; References; 6 Structural Optimization Under Uncertainty; 6.1 Problem Formulation; 6.2 Existence of Optimal Shapes; 6.3 Numerical Approximation via the LevelSet Method
 6.3.1 Computing Gradients of Shape Functionals; 6.3.2 Mise en Scène of the Level Set Method; 6.4 Numerical Simulation Results; 6.5 Notes and Related Software; References; 7 Miscellaneous Topics and Open Problems; 7.1 The Heat Equation Revisited II; 7.2 The BernoulliEuler Beam Equation Revisited II; 7.3 Concluding Remarks and Some Open Problems; References; Index
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319982090
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 on1050448291
 (OCoLC)1050448291
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