Control Of Partial Differential Equations
Download Control Of Partial Differential Equations full books in PDF, epub, and Kindle. Read online free Control Of Partial Differential Equations ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Optimal Control of Partial Differential Equations
Author | : Andrea Manzoni,Alfio Quarteroni,Sandro Salsa |
Publsiher | : Springer Nature |
Total Pages | : 507 |
Release | : 2022-01-01 |
Genre | : Mathematics |
ISBN | : 9783030772260 |
Download Optimal Control of Partial Differential Equations Book 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 of Partial Differential Equations
Author | : Fredi Tröltzsch |
Publsiher | : American Mathematical Society |
Total Pages | : 417 |
Release | : 2024-03-21 |
Genre | : Mathematics |
ISBN | : 9781470476441 |
Download Optimal Control of Partial Differential Equations Book 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.
Control of Partial Differential Equations
Author | : Giuseppe Da Prato,Luciano Tubaro |
Publsiher | : CRC Press |
Total Pages | : 302 |
Release | : 1994-08-19 |
Genre | : Mathematics |
ISBN | : 0824792408 |
Download Control of Partial Differential Equations Book in PDF, Epub and Kindle
This useful reference provides recent results as well as entirely new material on control problems for partial differential equations.
Optimization and Control for Partial Differential Equations
Author | : Roland Herzog,Matthias Heinkenschloss,Dante Kalise,Georg Stadler,Emmanuel Trélat |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 386 |
Release | : 2022-03-07 |
Genre | : Mathematics |
ISBN | : 9783110696004 |
Download Optimization and Control for Partial Differential Equations Book in PDF, Epub and Kindle
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.
Control Theory for Partial Differential Equations Volume 1 Abstract Parabolic Systems
Author | : Irena Lasiecka,Roberto Triggiani |
Publsiher | : Cambridge University Press |
Total Pages | : 678 |
Release | : 2000-02-13 |
Genre | : Mathematics |
ISBN | : 0521434084 |
Download Control Theory for Partial Differential Equations Volume 1 Abstract Parabolic Systems Book 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.
Controllability of Partial Differential Equations Governed by Multiplicative Controls
Author | : Alexander Y. Khapalov |
Publsiher | : Springer |
Total Pages | : 296 |
Release | : 2010-05-19 |
Genre | : Mathematics |
ISBN | : 9783642124136 |
Download Controllability of Partial Differential Equations Governed by Multiplicative Controls Book in PDF, Epub and Kindle
This monograph addresses the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The methodology is illustrated with a variety of model equations.
Control Theory of Partial Differential Equations
Author | : Guenter Leugering,Oleg Imanuvilov,Bing-Yu Zhang,Roberto Triggiani |
Publsiher | : CRC Press |
Total Pages | : 417 |
Release | : 2005-05-27 |
Genre | : Mathematics |
ISBN | : 9781420028317 |
Download Control Theory of Partial Differential Equations Book in PDF, Epub and Kindle
The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids a
Optimal Control of Systems Governed by Partial Differential Equations
Author | : Jacques Louis Lions |
Publsiher | : Springer |
Total Pages | : 400 |
Release | : 1971-01-01 |
Genre | : Mathematics |
ISBN | : 3540051155 |
Download Optimal Control of Systems Governed by Partial Differential Equations Book in PDF, Epub and Kindle
1. The development of a theory of optimal control (deterministic) requires the following initial data: (i) a control u belonging to some set ilIi ad (the set of 'admissible controls') which is at our disposition, (ii) for a given control u, the state y(u) of the system which is to be controlled is given by the solution of an equation (*) Ay(u)=given function ofu where A is an operator (assumed known) which specifies the system to be controlled (A is the 'model' of the system), (iii) the observation z(u) which is a function of y(u) (assumed to be known exactly; we consider only deterministic problems in this book), (iv) the "cost function" J(u) ("economic function") which is defined in terms of a numerical function z-+