The Resource Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures, Jesús Martínez-Frutos, Francisco Periago Esparza
Optimal control of PDEs under uncertainty : an introduction with application to optimal shape design of structures, Jesús Martínez-Frutos, 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 Martínez-Frutos, 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 Martínez-Frutos, 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 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 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 Laplace-Poisson Equation; 1.2.2 The Heat Equation; 1.2.3 The Bernoulli-Euler 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 Karhunen-Loève 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 Laplace-Poisson Equation Revisited I; 3.1.2 The Heat Equation Revisited I; 3.1.3 The Bernoulli-Euler 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 Risk-Averse Optimal Control; 3.4 Notes; References; 4 Numerical Resolution of Robust Optimal Control Problems
- 4.1 Finite-Dimensional Noise Assumption: From Random PDEs to Deterministic PDEs with a Finite-Dimensional Parameter4.2 Gradient-Based 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 One-Shot Methods; 4.5 Notes and Related Software; References; 5 Numerical Resolution of Risk Averse Optimal Control Problems; 5.1 An Adaptive, Gradient-Based, 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, Non-intrusive, 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 Level-Set 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 Bernoulli-Euler 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 Martínez-Frutos, 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 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 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
- Martínez-Frutos, 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 Martínez-Frutos, 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 Laplace-Poisson Equation; 1.2.2 The Heat Equation; 1.2.3 The Bernoulli-Euler 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 Karhunen-Loève 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 Laplace-Poisson Equation Revisited I; 3.1.2 The Heat Equation Revisited I; 3.1.3 The Bernoulli-Euler 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 Risk-Averse Optimal Control; 3.4 Notes; References; 4 Numerical Resolution of Robust Optimal Control Problems
- 4.1 Finite-Dimensional Noise Assumption: From Random PDEs to Deterministic PDEs with a Finite-Dimensional Parameter4.2 Gradient-Based 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 One-Shot Methods; 4.5 Notes and Related Software; References; 5 Numerical Resolution of Risk Averse Optimal Control Problems; 5.1 An Adaptive, Gradient-Based, 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, Non-intrusive, 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 Level-Set 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 Bernoulli-Euler 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 Martínez-Frutos, 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 Laplace-Poisson Equation; 1.2.2 The Heat Equation; 1.2.3 The Bernoulli-Euler 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 Karhunen-Loève 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 Laplace-Poisson Equation Revisited I; 3.1.2 The Heat Equation Revisited I; 3.1.3 The Bernoulli-Euler 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 Risk-Averse Optimal Control; 3.4 Notes; References; 4 Numerical Resolution of Robust Optimal Control Problems
- 4.1 Finite-Dimensional Noise Assumption: From Random PDEs to Deterministic PDEs with a Finite-Dimensional Parameter4.2 Gradient-Based 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 One-Shot Methods; 4.5 Notes and Related Software; References; 5 Numerical Resolution of Risk Averse Optimal Control Problems; 5.1 An Adaptive, Gradient-Based, 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, Non-intrusive, 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 Level-Set 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 Bernoulli-Euler 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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