Optimal Control Of Pdes Under Uncertainty
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Optimal Control Of Pdes Under Uncertainty
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Author : Jesús Martínez-Frutos
language : en
Publisher: Springer
Release Date : 2018-08-30
Optimal Control Of Pdes Under Uncertainty written by Jesús Martínez-Frutos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-30 with Mathematics categories.
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.
Optimization And Control For Partial Differential Equations
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Author : Roland Herzog
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-07
Optimization And Control For Partial Differential Equations written by Roland Herzog and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-07 with Mathematics categories.
This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.
Optimal Control Of Partial Differential Equations
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Author : Andrea Manzoni
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Optimal Control Of Partial Differential Equations written by Andrea Manzoni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Deterministic And Stochastic Optimal Control And Inverse Problems
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Author : Baasansuren Jadamba
language : en
Publisher: CRC Press
Release Date : 2021-12-15
Deterministic And Stochastic Optimal Control And Inverse Problems written by Baasansuren Jadamba and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-15 with Computers categories.
Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.
Optimal Control Expectations And Uncertainty
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Author : Sean Holly
language : en
Publisher: Cambridge University Press
Release Date : 1989-07-20
Optimal Control Expectations And Uncertainty written by Sean Holly and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-20 with Business & Economics categories.
An examination of how the rational expectations revolution and game theory have enhanced the understanding of how an economy functions.
Uncertain Optimal Control
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Author : Yuanguo Zhu
language : en
Publisher:
Release Date : 2019
Uncertain Optimal Control written by Yuanguo Zhu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with MATHEMATICS categories.
This book introduces the theory and applications of uncertain optimal control, and establishes two types of models including expected value uncertain optimal control and optimistic value uncertain optimal control. These models, which have continuous-time forms and discrete-time forms, make use of dynamic programming. The uncertain optimal control theory relates to equations of optimality, uncertain bang-bang optimal control, optimal control with switched uncertain system, and optimal control for uncertain system with time-delay. Uncertain optimal control has applications in portfolio selection, engineering, and games. The book is a useful resource for researchers, engineers, and students in the fields of mathematics, cybernetics, operations research, industrial engineering, artificial intelligence, economics, and management science.
Constrained Optimization And Optimal Control For Partial Differential Equations
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Author : Günter Leugering
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-03
Constrained Optimization And Optimal Control For Partial Differential Equations written by Günter Leugering and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-03 with Mathematics categories.
This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Mathematical Analysis In Interdisciplinary Research
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Author : Ioannis N. Parasidis
language : en
Publisher: Springer Nature
Release Date : 2022-03-10
Mathematical Analysis In Interdisciplinary Research written by Ioannis N. Parasidis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Mathematics categories.
This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.
Recent Advances In Pdes Analysis Numerics And Control
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Author : Anna Doubova
language : en
Publisher: Springer
Release Date : 2018-11-02
Recent Advances In Pdes Analysis Numerics And Control written by Anna Doubova and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.
This book contains the main results of the talks given at the workshop “Recent Advances in PDEs: Analysis, Numerics and Control”, which took place in Sevilla (Spain) on January 25-27, 2017. The work comprises 12 contributions given by high-level researchers in the partial differential equation (PDE) area to celebrate the 60th anniversary of Enrique Fernández-Cara (University of Sevilla). The main topics covered here are: Control and inverse problems, Analysis of Fluid mechanics and Numerical Analysis. The work is devoted to researchers in these fields.
Mathematical And Computational Methods For Modelling Approximation And Simulation
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Author : Domingo Barrera
language : en
Publisher: Springer Nature
Release Date : 2022-05-08
Mathematical And Computational Methods For Modelling Approximation And Simulation written by Domingo Barrera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-08 with Mathematics categories.
This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models. The book includes nine contributions, mostly related to quasi-interpolation. This is a topic that continues to register a high level of interest, both for those working in the field of approximation theory and for those interested in its use in a practical context. Two chapters address the construction of quasi-interpolants, and three others focus on the use of quasi-interpolation in solving integral equations. The remaining four concern a problem related to the heat diffusion equation, new results on the notion of convexity in probabilistic metric spaces (which are applied to the study of the existence and uniqueness of the solution of a Volterra equation), the use of smoothing splines to address an economic problem and, finally, the analysis of poverty measures, which is a topic of increased interest to society. The book is addressed to researchers interested in Applied Mathematics, with particular reference to the aforementioned topics.