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Author | : John A. Burns |
Publisher | : CRC Press |
Total Pages | : 562 |
Release | : 2013-08-28 |
Genre | : Mathematics |
ISBN | : 1466571403 |
Download Introduction to the Calculus of Variations and Control with Modern Applications Book in PDF, ePub and Kindle
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions a
Author | : Charles R. MacCluer |
Publisher | : Courier Corporation |
Total Pages | : 274 |
Release | : 2013-05-20 |
Genre | : Mathematics |
ISBN | : 0486278301 |
Download Calculus of Variations Book in PDF, ePub and Kindle
First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.
Author | : Mike Mesterton-Gibbons |
Publisher | : American Mathematical Soc. |
Total Pages | : 274 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821847724 |
Download A Primer on the Calculus of Variations and Optimal Control Theory Book in PDF, ePub and Kindle
The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.
Author | : Hans Sagan |
Publisher | : Courier Corporation |
Total Pages | : 484 |
Release | : 2012-04-26 |
Genre | : Mathematics |
ISBN | : 048613802X |
Download Introduction to the Calculus of Variations Book in PDF, ePub and Kindle
Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Author | : Daniel Liberzon |
Publisher | : Princeton University Press |
Total Pages | : 255 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 0691151873 |
Download Calculus of Variations and Optimal Control Theory Book in PDF, ePub and Kindle
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Author | : Irene Fonseca |
Publisher | : Springer Science & Business Media |
Total Pages | : 602 |
Release | : 2007-08-22 |
Genre | : Science |
ISBN | : 0387690069 |
Download Modern Methods in the Calculus of Variations Book in PDF, ePub and Kindle
This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.
Author | : John A. Burns |
Publisher | : CRC Press |
Total Pages | : 564 |
Release | : 2013-08-28 |
Genre | : Mathematics |
ISBN | : 146657139X |
Download Introduction to the Calculus of Variations and Control with Modern Applications Book in PDF, ePub and Kindle
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.
Author | : Frederic Wan |
Publisher | : Routledge |
Total Pages | : 660 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 1351436511 |
Download Introduction To The Calculus of Variations And Its Applications Book in PDF, ePub and Kindle
This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.
Author | : Hansjörg Kielhöfer |
Publisher | : Springer |
Total Pages | : 242 |
Release | : 2018-01-25 |
Genre | : Mathematics |
ISBN | : 3319711237 |
Download Calculus of Variations Book in PDF, ePub and Kindle
This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.
Author | : L. P. Lebedev |
Publisher | : World Scientific |
Total Pages | : 435 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9812794999 |
Download The Calculus of Variations and Functional Analysis Book in PDF, ePub and Kindle
This volume is aimed at those who are concerned about Chinese medicine - how it works, what its current state is and, most important, how to make full use of it. The audience therefore includes clinicians who want to serve their patients better and patients who are eager to supplement their own conventional treatment. The authors of the book belong to three different fields, modern medicine, Chinese medicine and pharmacology. They provide information from their areas of expertise and concern, attempting to make it comprehensive for users. The approach is macroscopic and philosophical; readers convinced of the philosophy are to seek specific assistance.