Lectures On The Calculus Of Variations And Optimal Control Theory
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Lectures On The Calculus Of Variations And Optimal Control Theory
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Author : Laurence Chisholm Young
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Lectures On The Calculus Of Variations And Optimal Control Theory written by Laurence Chisholm Young and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Lectures On The Calculus Of Variations And Optimal Control Theory
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Author : Laurence C. Young
language : en
Publisher:
Release Date : 1962
Lectures On The Calculus Of Variations And Optimal Control Theory written by Laurence C. Young and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Calculus of variations categories.
Lectures On The Calculus Of Variations And Optimal Control Theory Calculus Of Variations And Optimal Control Theory
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Author : Laurence Chisholm Young
language : en
Publisher:
Release Date : 1969
Lectures On The Calculus Of Variations And Optimal Control Theory Calculus Of Variations And Optimal Control Theory written by Laurence Chisholm Young and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
Lectures On The Calculus Of Variations And Optimal Control Theory
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Author : L. C. Young
language : en
Publisher:
Release Date :
Lectures On The Calculus Of Variations And Optimal Control Theory written by L. C. Young and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
A Primer On The Calculus Of Variations And Optimal Control Theory
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Author : Mike Mesterton-Gibbons
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
A Primer On The Calculus Of Variations And Optimal Control Theory written by Mike Mesterton-Gibbons and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
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
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Author : Daniel Liberzon
language : en
Publisher: Princeton University Press
Release Date : 2012
Calculus Of Variations And Optimal Control Theory written by Daniel Liberzon and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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
Lecture On The Calculus Of Variations And Optimal Control Theory
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Author : L. C. Young
language : en
Publisher:
Release Date : 2000
Lecture On The Calculus Of Variations And Optimal Control Theory written by L. C. Young and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Calculus Of Variations And Optimal Control Theory
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Author : Magnus Rudolph Hestenes
language : en
Publisher:
Release Date : 1980
Calculus Of Variations And Optimal Control Theory written by Magnus Rudolph Hestenes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Constrained Optimization In The Calculus Of Variations And Optimal Control Theory
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Author : J Gregory
language : en
Publisher: CRC Press
Release Date : 2018-01-18
Constrained Optimization In The Calculus Of Variations And Optimal Control Theory written by J Gregory and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.
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.
Calculus Of Variations And Optimal Control
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Author : N. P. Osmolovskii
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-08-18
Calculus Of Variations And Optimal Control written by N. P. Osmolovskii and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-18 with Mathematics categories.
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.