Control Theory Of Partial Differential Equations PDF Download
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Author | : Irena Lasiecka |
Publisher | : Cambridge University Press |
Total Pages | : 678 |
Release | : 2000-02-13 |
Genre | : Mathematics |
ISBN | : 9780521434089 |
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.
Author | : Guenter Leugering |
Publisher | : CRC Press |
Total Pages | : 417 |
Release | : 2005-05-27 |
Genre | : Mathematics |
ISBN | : 1420028316 |
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
Author | : Fatiha Alabau-Boussouira |
Publisher | : Springer |
Total Pages | : 276 |
Release | : 2019-07-04 |
Genre | : Mathematics |
ISBN | : 3030179494 |
Download Trends in Control Theory and Partial Differential Equations Book in PDF, ePub and Kindle
This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.
Author | : Fredi Tröltzsch |
Publisher | : American Mathematical Society |
Total Pages | : 417 |
Release | : 2024-03-21 |
Genre | : Mathematics |
ISBN | : 1470476444 |
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.
Author | : J. F. Pommaret |
Publisher | : Springer Science & Business Media |
Total Pages | : 578 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 9780792370352 |
Download Partial Differential Control Theory Book in PDF, ePub and Kindle
Algebraic analysis, that is the algebraic study of systems of partial differential equations by means of module theory and homological algebra, was pioneered around 1970 by M. Kashiwara, B. Malgrange, and V.P. Palamodov. The theory of differential modules, namely modules over a noncommutative ring of differential operators, is a fashionable subject of research today. However, despite its fundamental importance in mathematics, it can only be found in specialist books and papers, and has only been applied in control theory since 1990. This book provides an account of algebraic analysis and its application to control systems defined by partial differential equations. The first volume presents the mathematical tools needed from both commutative algebra, homological algebra, differential geometry and differential algebra. The second volume applies these new methods in order to study the structural and input/output properties of both linear and nonlinear control systems. Hundreds of explicit examples allow the reader to gain insight and experience in these topics.
Author | : A.K. Aziz |
Publisher | : Academic Press |
Total Pages | : 289 |
Release | : 2014-05-10 |
Genre | : Technology & Engineering |
ISBN | : 1483216306 |
Download Control Theory of Systems Governed by Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Andrea Manzoni |
Publisher | : Springer Nature |
Total Pages | : 507 |
Release | : 2022-01-01 |
Genre | : Mathematics |
ISBN | : 3030772268 |
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.
Author | : Miroslav Krstic |
Publisher | : SIAM |
Total Pages | : 197 |
Release | : 2008-01-01 |
Genre | : Mathematics |
ISBN | : 0898718600 |
Download Boundary Control of PDEs Book in PDF, ePub and Kindle
The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.
Author | : Irena Lasiecka |
Publisher | : SIAM |
Total Pages | : 256 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9780898717099 |
Download Mathematical Control of Coupled PDEs Book in PDF, ePub and Kindle
Author | : Concepción Muriel |
Publisher | : Springer Nature |
Total Pages | : 102 |
Release | : 2021-03-13 |
Genre | : Mathematics |
ISBN | : 3030618757 |
Download Recent Advances in Differential Equations and Control Theory Book in PDF, ePub and Kindle
This book collects the latest results and new trends in the application of mathematics to some problems in control theory, numerical simulation and differential equations. The work comprises the main results presented at a thematic minisymposium, part of the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), held in Valencia, Spain, from 15 to 18 July 2019. The topics covered in the 6 peer-review contributions involve applications of numerical methods to real problems in oceanography and naval engineering, as well as relevant results on switching control techniques, which can have multiple applications in industrial complexes, electromechanical machines, biological systems, etc. Problems in control theory, as in most engineering problems, are modeled by differential equations, for which standard solving procedures may be insufficient. The book also includes recent geometric and analytical methods for the search of exact solutions for differential equations, which serve as essential tools for analyzing problems in many scientific disciplines.