Classical Mechanics With Calculus Of Variations And Optimal Control

Classical Mechanics With Calculus Of Variations And Optimal Control Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Classical Mechanics With Calculus Of Variations And Optimal Control book. This book definitely worth reading, it is an incredibly well-written.

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 : 322 pages
File Size : 40,5 Mb
Release : 2014-03-07
Category : Mathematics
ISBN : 9780821891384

Get Book

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.

Calculus Of Variations And Functional Analysis, The: With Optimal Control And Applications In Mechanics

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

Author : Lebedev Leonid P,Cloud Michael J
Publisher : World Scientific
Page : 436 pages
File Size : 44,7 Mb
Release : 2003-12-23
Category : Technology & Engineering
ISBN : 9789814485173

Get Book

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.

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 : 50,8 Mb
Release : 2009
Category : Calculus of variations
ISBN : 9780821847725

Get Book

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.

The Calculus of Variations and Functional Analysis

L. P. Lebedev,Michael J. Cloud
The Calculus of Variations and Functional Analysis Book PDF

Author : L. P. Lebedev,Michael J. Cloud
Publisher : World Scientific
Page : 435 pages
File Size : 42,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812385819

Get Book

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.

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 : 42,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489903334

Get Book

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.

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 : 48,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691151878

Get Book

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

Calculus of Variations

Charles R. MacCluer
Calculus of Variations Book PDF

Author : Charles R. MacCluer
Publisher : Courier Corporation
Page : 272 pages
File Size : 50,8 Mb
Release : 2013-05-20
Category : Mathematics
ISBN : 9780486278308

Get Book

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.

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 : 47,5 Mb
Release : 1998-08-18
Category : Mathematics
ISBN : 082189787X

Get Book

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.

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 : 232 pages
File Size : 55,5 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351079310

Get Book

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.

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 : 44,7 Mb
Release : 2013-02-06
Category : Mathematics
ISBN : 9781447148203

Get Book

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.

Calculus of Variations and Optimal Control/Differential Equations Set

Alexander Ioffe,Simeon Reich,I Shafrir
Calculus of Variations and Optimal Control Differential Equations Set Book PDF

Author : Alexander Ioffe,Simeon Reich,I Shafrir
Publisher : CRC Press
Page : 346 pages
File Size : 50,7 Mb
Release : 1999-07-16
Category : Mathematics
ISBN : 9781584881407

Get Book

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.

Optimal Control of Mechanical Oscillations

Agnessa Kovaleva
Optimal Control of Mechanical Oscillations Book PDF

Author : Agnessa Kovaleva
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 47,5 Mb
Release : 2013-04-17
Category : Technology & Engineering
ISBN : 9783540492580

Get Book

Optimal Control of Mechanical Oscillations by Agnessa Kovaleva Pdf

This book explores two important aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and control possibilities for random disturbances. The main content of the book is based upon assertions of the optimal control theory and the disturbance theory. All theoretical propositions are illustrated by examples with exact mechanical context. An appendix covers the necessary mathematical prerequisites.

Lectures on the Calculus of Variations and Optimal Control Theory

Laurence Chisholm Young
Lectures on the Calculus of Variations and Optimal Control Theory Book PDF

Author : Laurence Chisholm Young
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 40,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0821826905

Get Book

Lectures on the Calculus of Variations and Optimal Control Theory by Laurence Chisholm Young Pdf

This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and "automatic" existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.

Optimal Control Via Nonsmooth Analysis

Philip Daniel Loewen
Optimal Control Via Nonsmooth Analysis Book PDF

Author : Philip Daniel Loewen
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 46,6 Mb
Release : 1993
Category : Control theory
ISBN : 0821869965

Get Book

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.

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 : 48,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780198514893

Get Book

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.