Optimal Control of Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Control of Partial Differential Equations write by Fredi Tröltzsch. This book was released on 2024-03-21. Optimal Control of Partial Differential Equations available in PDF, EPUB and Kindle. Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.
Optimal Control of Partial Differential Equations II: Theory and Applications
Optimal Control of Partial Differential Equations II: Theory and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Control of Partial Differential Equations II: Theory and Applications write by K.-H. Hoffmann. This book was released on 2013-03-14. Optimal Control of Partial Differential Equations II: Theory and Applications available in PDF, EPUB and Kindle. This volume contains the contributions of participants of the conference "Optimal Control of Partial Differential Equations" which, under the chairmanship of the editors, took place at the Mathematisches Forschungsinstitut Oberwolfach from May 18 to May 24, 1986. The great variety of topics covered by the contributions strongly indicates that also in the future it will be impossible to develop a unifying control theory of partial differential equations. On the other hand, there is a strong tendency to treat prob lems which are directly connected to practical applications. So this volume contains real-world applications like optimal cooling laws for the production of rolled steel or concrete solutions for the problem of optimal shape design in mechanics and hydrody namics. Another main topic is the construction of numerical methods. This includes applications of the finite element method as well as of Quasi-Newton-methods to con strained and unconstrained control problems. Also, very complex problems arising in the theory of free boundary value problems are treated. ]~inally, some contribu tions show how practical problems stimulate the further development of the theory; in particular, this is the case for fields like suboptimal control, necessary optimality conditions and sensitivity analysis. As usual, the lectures and stimulating discussions took place in the pleasant at mosphere of the Mathematisches Forschungsinstitut Oberwolfach. Special thanks of the participants are returned to the Director as well as to the staff of the institute.
Optimal Control of Partial Differential Equations
Optimal Control of Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Control of Partial Differential Equations write by Andrea Manzoni. This book was released on 2022-01-01. Optimal Control of Partial Differential Equations available in PDF, EPUB and Kindle. 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.
Optimal Control Theory for Applications
Optimal Control Theory for Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Control Theory for Applications write by David G. Hull. This book was released on 2013-03-09. Optimal Control Theory for Applications available in PDF, EPUB and Kindle. The published material represents the outgrowth of teaching analytical optimization to aerospace engineering graduate students. To make the material available to the widest audience, the prerequisites are limited to calculus and differential equations. It is also a book about the mathematical aspects of optimal control theory. It was developed in an engineering environment from material learned by the author while applying it to the solution of engineering problems. One goal of the book is to help engineering graduate students learn the fundamentals which are needed to apply the methods to engineering problems. The examples are from geometry and elementary dynamical systems so that they can be understood by all engineering students. Another goal of this text is to unify optimization by using the differential of calculus to create the Taylor series expansions needed to derive the optimality conditions of optimal control theory.
Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems
Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems write by Irena Lasiecka. This book was released on 2000-02-13. Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems available in PDF, EPUB and Kindle. First of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations, originally published in 2000.
