Optimal Control Problems For Partial Differential Equations On Reticulated Domains

Author : Peter I. Kogut,Günter R. Leugering
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 40,5 Mb
Release : 2011-09-09
Category : Science
ISBN : 9780817681494

Get Book

Optimal Control Problems for Partial Differential Equations on Reticulated Domains by Peter I. Kogut,Günter R. Leugering Pdf

In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains.

Author : John E. Lagnese,Günter Leugering
Publisher : Birkhäuser
Page : 443 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878852

Get Book

Domain Decomposition Methods in Optimal Control of Partial Differential Equations by John E. Lagnese,Günter Leugering Pdf

While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations. This monograph emphasizes domain decomposition methods in the context of so-called virtual optimal control problems and treats optimal control problems for partial differential equations and their decompositions using an all-at-once approach.

Author : Andrea Manzoni,Alfio Quarteroni,Sandro Salsa
Publisher : Springer Nature
Page : 507 pages
File Size : 54,9 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030772260

Get Book

Optimal Control of Partial Differential Equations by Andrea Manzoni,Alfio Quarteroni,Sandro Salsa Pdf

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.

Author : Roland Herzog,Matthias Heinkenschloss,Dante Kalise,Georg Stadler,Emmanuel Trélat
Publisher : Walter de Gruyter GmbH & Co KG
Page : 474 pages
File Size : 41,5 Mb
Release : 2022-03-07
Category : Mathematics
ISBN : 9783110695984

Get Book

Optimization and Control for Partial Differential Equations by Roland Herzog,Matthias Heinkenschloss,Dante Kalise,Georg Stadler,Emmanuel Trélat Pdf

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.

Author : Fredi Tröltzsch
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 41,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849040

Get Book

Optimal Control of Partial Differential Equations by Fredi Tröltzsch Pdf

Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. It includes topics on the existence of optimal solutions.

Author : Kristian Bredies,Christian Clason,Karl Kunisch,Gregory von Winckel
Publisher : Birkhäuser
Page : 215 pages
File Size : 41,6 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 3034806329

Get Book

Control and Optimization with PDE Constraints by Kristian Bredies,Christian Clason,Karl Kunisch,Gregory von Winckel Pdf

Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full spectrum from analysis to numerical realization and applications. Leading scientists address current topics such as non-smooth optimization, Hamilton–Jacobi–Bellmann equations, issues in optimization and control of stochastic partial differential equations, reduced-order models and domain decomposition, discretization error estimates for optimal control problems, and control of quantum-dynamical systems. These contributions originate from the “International Workshop on Control and Optimization of PDEs” in Mariatrost in October 2011. This book is an excellent resource for students and researchers in control or optimization of differential equations. Readers interested in theory or in numerical algorithms will find this book equally useful.

Author : Karl-Heinz Hoffmann,Günter Leugering,Fredi Tröltzsch
Publisher : Birkhäuser
Page : 324 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886918

Get Book

Optimal Control of Partial Differential Equations by Karl-Heinz Hoffmann,Günter Leugering,Fredi Tröltzsch Pdf

The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathematicians and scientists working in the field.

Author : A.K. Aziz,J.W. Wingate,M.J. Balas
Publisher : Academic Press
Page : 289 pages
File Size : 41,9 Mb
Release : 2014-05-10
Category : Technology & Engineering
ISBN : 9781483216300

Get Book

Control Theory of Systems Governed by Partial Differential Equations by A.K. Aziz,J.W. Wingate,M.J. Balas Pdf

Control Theory of Systems Governed by Partial Differential Equations covers the proceedings of the 1976 Conference by the same title, held at the Naval Surface Weapons Center, Silver Spring, Maryland. The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type. This chapter also explores the control of free surfaces and the geometrical control variables. The last chapter provides a summary of the features and applications of the numerical approximation of problems of optimal control. This book will prove useful to mathematicians, engineers, and researchers.

Author : Anonim
Publisher : Elsevier
Page : 596 pages
File Size : 54,5 Mb
Release : 2022-02-15
Category : Mathematics
ISBN : 9780323853392

Get Book

Numerical Control: Part A by Anonim Pdf

Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control

Author : Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 41,7 Mb
Release : 2012-01-03
Category : Mathematics
ISBN : 9783034801331

Get Book

Constrained Optimization and Optimal Control for Partial Differential Equations by Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich Pdf

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.

Author : Irwin Yousept
Publisher : Cuvillier Verlag
Page : 26 pages
File Size : 41,9 Mb
Release : 2008
Category : Electronic
ISBN : 9783867276689

Get Book

Optimal Control of Partial Differential Equations Involving Pointwise State Constraints: Regularization and Applications by Irwin Yousept Pdf

Author : Victor A. Sadovnichiy,Michael Z. Zgurovsky
Publisher : Springer Nature
Page : 525 pages
File Size : 53,5 Mb
Release : 2020-11-24
Category : Mathematics
ISBN : 9783030503024

Get Book

Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics by Victor A. Sadovnichiy,Michael Z. Zgurovsky Pdf

This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields

Author : Volker Schulz,Diaraf Seck
Publisher : Springer
Page : 275 pages
File Size : 51,5 Mb
Release : 2018-09-05
Category : Mathematics
ISBN : 9783319904696

Get Book

Shape Optimization, Homogenization and Optimal Control by Volker Schulz,Diaraf Seck Pdf

The contributions in this volume give an insight into current research activities in Shape Optimization, Homogenization and Optimal Control performed in Africa, Germany and internationally. Seeds for collaboration can be found in the first four papers in the field of homogenization. Modelling and optimal control in partial differential equations is the topic of the next six papers, again mixed from Africa and Germany. Finally, new results in the field of shape optimization are discussed in the final international three papers. This workshop, held at the AIMS Center Senegal, March 13-16, 2017, has been supported by the Deutsche Forschungsgemeinschaft (DFG) and by the African Institute for Mathematical Sciences (AIMS) in Senegal, which is one of six centres of a pan-African network of centres of excellence for postgraduate education, research and outreach in mathematical sciences.

Author : Baasansuren Jadamba,Akhtar A. Khan,Stanisław Migórski,Miguel Sama
Publisher : CRC Press
Page : 394 pages
File Size : 52,7 Mb
Release : 2021-12-15
Category : Computers
ISBN : 9781000511727

Get Book

Deterministic and Stochastic Optimal Control and Inverse Problems by Baasansuren Jadamba,Akhtar A. Khan,Stanisław Migórski,Miguel Sama Pdf

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.

Author : Peter I. Kogut,Olga P. Kupenko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 351 pages
File Size : 53,5 Mb
Release : 2019-12-02
Category : Mathematics
ISBN : 9783110668520

Get Book

Approximation Methods in Optimization of Nonlinear Systems by Peter I. Kogut,Olga P. Kupenko Pdf

The monograph addresses some problems particularly with regard to ill-posedness of boundary value problems and problems where we cannot expect to have uniqueness of their solutions in the standard functional spaces. Bringing original and previous results together, it tackles computational challenges by exploiting methods of approximation and asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs