Functional Analysis Calculus Of Variations And Optimal Control

Author : Francis Clarke
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 55,5 Mb
Release : 2013-02-06
Category : Mathematics
ISBN : 9781447148203

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Functional Analysis, Calculus of Variations and Optimal Control by Francis Clarke Pdf

Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

Author : Springer
Publisher : Unknown
Page : 608 pages
File Size : 51,8 Mb
Release : 2013-02-05
Category : Electronic
ISBN : 1447148215

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Functional Analysis, Calculus of Variations and Optimal Control by Springer Pdf

Author : L. P. Lebedev,Michael J. Cloud
Publisher : World Scientific
Page : 435 pages
File Size : 51,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812385819

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The Calculus of Variations and Functional Analysis by L. P. Lebedev,Michael J. Cloud Pdf

In this book, Sam helps his goose sisters fly to safety to looking for familiar landforms.

Author : Lebedev Leonid P,Cloud Michael J
Publisher : World Scientific
Page : 436 pages
File Size : 43,6 Mb
Release : 2003-12-23
Category : Technology & Engineering
ISBN : 9789814485173

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Calculus Of Variations And Functional Analysis, The: With Optimal Control And Applications In Mechanics by Lebedev Leonid P,Cloud Michael J Pdf

This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of “the calculus of variations”) and more modern topics (under the heading of “optimal control”). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.

Author : Daniel Liberzon
Publisher : Princeton University Press
Page : 255 pages
File Size : 48,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691151878

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Calculus of Variations and Optimal Control Theory by Daniel Liberzon Pdf

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 : Alexander J. Zaslavski
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 50,9 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461473787

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Nonconvex Optimal Control and Variational Problems by Alexander J. Zaslavski Pdf

Nonconvex Optimal Control and Variational Problems is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems. Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with “good” functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author. This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community.

Author : Leonid P. Lebedev
Publisher : Unknown
Page : 0 pages
File Size : 47,9 Mb
Release : 2012
Category : Electronic
ISBN : 981439047X

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Advanced Engineering Analysis by Leonid P. Lebedev Pdf

Annotation Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study.

Author : N. P. Osmolovskii
Publisher : American Mathematical Soc.
Page : 392 pages
File Size : 49,9 Mb
Release : 1998-08-18
Category : Mathematics
ISBN : 082189787X

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Calculus of Variations and Optimal Control by N. P. Osmolovskii Pdf

The theory of a Pontryagin minimum is developed for problems in the calculus of variations. The application of the notion of a Pontryagin minimum to the calculus of variations is a distinctive feature of this book. A new theory of quadratic conditions for a Pontryagin minimum, which covers broken extremals, is developed, and corresponding sufficient conditions for a strong minimum are obtained. Some classical theorems of the calculus of variations are generalized.

Author : Philip Daniel Loewen
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 41,5 Mb
Release : 1993
Category : Control theory
ISBN : 0821869965

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Optimal Control Via Nonsmooth Analysis by Philip Daniel Loewen Pdf

This book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control. Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher.

Author : George Leitmann
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 55,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489903334

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The Calculus of Variations and Optimal Control by George Leitmann Pdf

When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

Author : Enid R. Pinch
Publisher : Oxford University Press
Page : 245 pages
File Size : 40,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780198514893

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Optimal Control and the Calculus of Variations by Enid R. Pinch Pdf

A paperback edition of this successful textbook for final year undergraduate mathematicians and control engineering students, this book contains exercises and many worked examples, with complete solutions and hints making it ideal not only as a class textbook but also for individual study. Theintorduction to optimal control begins by considering the problem of minimizing a function of many variables, before moving on to the main subject: the optimal control of systems governed by ordinary differential equations.

Author : L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev
Publisher : World Scientific
Page : 500 pages
File Size : 55,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814390477

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Advanced Engineering Analysis by L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev Pdf

Advanced Engineering Analysis: The Calculus of Variations and Functional Analysis with Applications in Mechanics Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study. Book jacket.

Author : Morton I. Kamien,Nancy L. Schwartz
Publisher : Courier Corporation
Page : 402 pages
File Size : 49,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9780486310282

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Dynamic Optimization, Second Edition by Morton I. Kamien,Nancy L. Schwartz Pdf

Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

Author : Alexander Ioffe,Simeon Reich,I Shafrir
Publisher : CRC Press
Page : 346 pages
File Size : 54,6 Mb
Release : 1999-07-16
Category : Mathematics
ISBN : 9781584881407

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Calculus of Variations and Optimal Control/Differential Equations Set by Alexander Ioffe,Simeon Reich,I Shafrir Pdf

The calculus of variations is a classical area of mathematical analysis yet its myriad applications in science and technology continue to keep it an active area of research. Encompassing two volumes, this set brings together leading experts who focus on critical point theory, differential equations, and the variational aspects of optimal control. The books cover monotonicity, nonlinear optimization, the impossible pilot wave, the Lavrentiev phenomenon, and elliptic problems.

Author : Alexander Zaslavski
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 43,9 Mb
Release : 2005-08-25
Category : Mathematics
ISBN : 038728155X

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Turnpike Properties in the Calculus of Variations and Optimal Control by Alexander Zaslavski Pdf

This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics. Audience This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics.