The Calculus Of Variations And Optimal Control

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A Primer on the Calculus of Variations and Optimal Control Theory

Mike Mesterton-Gibbons
A Primer on the Calculus of Variations and Optimal Control Theory Book PDF

Author : Mike Mesterton-Gibbons
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 46,5 Mb
Release : 2009
Category : Calculus of variations
ISBN : 9780821847725

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A Primer on the Calculus of Variations and Optimal Control Theory by Mike Mesterton-Gibbons Pdf

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.

Calculus of Variations and Optimal Control Theory

Daniel Liberzon
Calculus of Variations and Optimal Control Theory Book PDF

Author : Daniel Liberzon
Publisher : Princeton University Press
Page : 255 pages
File Size : 49,9 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

The Calculus of Variations and Optimal Control

George Leitmann
The Calculus of Variations and Optimal Control Book PDF

Author : George Leitmann
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 46,8 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.

Functional Analysis, Calculus of Variations and Optimal Control

Francis Clarke
Functional Analysis Calculus of Variations and Optimal Control Book PDF

Author : Francis Clarke
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 54,5 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.

Classical Mechanics with Calculus of Variations and Optimal Control

Mark Levi
Classical Mechanics with Calculus of Variations and Optimal Control Book PDF

Author : Mark Levi
Publisher : American Mathematical Soc.
Page : 299 pages
File Size : 44,6 Mb
Release : 2014-03-07
Category : Mathematics
ISBN : 9780821891384

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Classical Mechanics with Calculus of Variations and Optimal Control by Mark Levi Pdf

This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

Dynamic Optimization, Second Edition

Morton I. Kamien,Nancy L. Schwartz
Dynamic Optimization Second Edition Book PDF

Author : Morton I. Kamien,Nancy L. Schwartz
Publisher : Courier Corporation
Page : 402 pages
File Size : 54,6 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.

Optimal Control and the Calculus of Variations

Enid R. Pinch
Optimal Control and the Calculus of Variations Book PDF

Author : Enid R. Pinch
Publisher : Oxford University Press
Page : 245 pages
File Size : 45,6 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.

Constrained Optimization In The Calculus Of Variations and Optimal Control Theory

J Gregory
Constrained Optimization In The Calculus Of Variations and Optimal Control Theory Book PDF

Author : J Gregory
Publisher : CRC Press
Page : 242 pages
File Size : 51,8 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351087766

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Constrained Optimization In The Calculus Of Variations and Optimal Control Theory by J Gregory Pdf

The major purpose of this book is to present the theoretical ideas and the analytical and numerical methods to enable the reader to understand and efficiently solve these important optimizational problems.The first half of this book should serve as the major component of a classical one or two semester course in the calculus of variations and optimal control theory. The second half of the book will describe the current research of the authors which is directed to solving these problems numerically. In particular, we present new reformulations of constrained problems which leads to unconstrained problems in the calculus of variations and new general, accurate and efficient numerical methods to solve the reformulated problems. We believe that these new methods will allow the reader to solve important problems.

Turnpike Properties in the Calculus of Variations and Optimal Control

Alexander Zaslavski
Turnpike Properties in the Calculus of Variations and Optimal Control Book PDF

Author : Alexander Zaslavski
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 50,7 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.

Variational Calculus with Elementary Convexity

J.L. Troutman
Variational Calculus with Elementary Convexity Book PDF

Author : J.L. Troutman
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468401585

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Variational Calculus with Elementary Convexity by J.L. Troutman Pdf

The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.

Calculus of Variations

Charles R. MacCluer
Calculus of Variations Book PDF

Author : Charles R. MacCluer
Publisher : Courier Corporation
Page : 272 pages
File Size : 42,9 Mb
Release : 2013-05-20
Category : Mathematics
ISBN : 9780486278308

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Calculus of Variations by Charles R. MacCluer Pdf

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.

Introduction to the Calculus of Variations and Control with Modern Applications

John A. Burns
Introduction to the Calculus of Variations and Control with Modern Applications Book PDF

Author : John A. Burns
Publisher : CRC Press
Page : 562 pages
File Size : 53,8 Mb
Release : 2013-08-28
Category : Mathematics
ISBN : 9781466571402

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Introduction to the Calculus of Variations and Control with Modern Applications by John A. Burns Pdf

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

Calculus of Variations and Optimal Control

N. P. Osmolovskii
Calculus of Variations and Optimal Control Book PDF

Author : N. P. Osmolovskii
Publisher : American Mathematical Soc.
Page : 392 pages
File Size : 42,5 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.

The Calculus of Variations

Bruce van Brunt
The Calculus of Variations Book PDF

Author : Bruce van Brunt
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 40,8 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216973

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The Calculus of Variations by Bruce van Brunt Pdf

Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.

Introduction to the Calculus of Variations

Hans Sagan
Introduction to the Calculus of Variations Book PDF

Author : Hans Sagan
Publisher : Courier Corporation
Page : 484 pages
File Size : 42,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138022

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Introduction to the Calculus of Variations by Hans Sagan Pdf

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.