Applications Of Variational Calculus In Optimal Control
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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
Introduction To The Calculus Of Variations And Control With Modern Applications
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Author : John A. Burns
language : en
Publisher: CRC Press
Release Date : 2013-08-28
Introduction To The Calculus Of Variations And Control With Modern Applications written by John A. Burns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-28 with Mathematics categories.
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
Turnpike Properties In The Calculus Of Variations And Optimal Control
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-27
Turnpike Properties In The Calculus Of Variations And Optimal Control written by Alexander J. Zaslavski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-27 with Mathematics categories.
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.
Functional Analysis Calculus Of Variations And Optimal Control
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Author : Francis Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-06
Functional Analysis Calculus Of Variations And Optimal Control written by Francis Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-06 with Mathematics categories.
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.
Optimal Control With Engineering Applications
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Author : Hans P. Geering
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-23
Optimal Control With Engineering Applications written by Hans P. Geering and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-23 with Technology & Engineering categories.
This book introduces a variety of problem statements in classical optimal control, in optimal estimation and filtering, and in optimal control problems with non-scalar-valued performance criteria. Many example problems are solved completely in the body of the text. All chapter-end exercises are sketched in the appendix. The theoretical part of the book is based on the calculus of variations, so the exposition is very transparent and requires little mathematical rigor.
Applications Of Variational Calculus In Optimal Control
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Author : Ellsworth Ingle
language : en
Publisher:
Release Date : 2025-04-20
Applications Of Variational Calculus In Optimal Control written by Ellsworth Ingle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-20 with Technology & Engineering categories.
Embark on a transformative journey into the heart of optimal control with "Applications of Variational Calculus in Optimal Control: Exploring problems of minimization, dynamic programming, and feedback control." This book is your definitive guide, meticulously crafted to unravel the complexities of variational calculus and its profound applications in the realm of optimal control. From foundational principles to cutting-edge techniques, prepare to **master** the art of optimizing dynamic systems. Begin your exploration with a rigorous "Introduction to Variational Calculus," where you will lay a solid foundation in the fundamental concepts. You'll learn how to pinpoint functions that minimize functionals, unlocking the secrets behind the Euler-Lagrange equation - a pivotal tool for solving basic optimization problems that form the bedrock of more intricate control scenarios. This chapter meticulously prepares you for the advanced topics that await. Next, delve into "Optimal Control Problems," where you'll encounter the formal mathematical structure for tackling complex control challenges. Learn to define the architecture of a general optimal control problem, specifying the objective function, dynamic constraints, and boundary conditions with precision. Explore necessary and sufficient conditions, including extended Euler-Lagrange equations, to ensure you can identify and guarantee optimal solutions. Uncover the power of "Dynamic Programming Approach" and witness the magic of Bellman's principle of optimality. Grasp the Hamilton-Jacobi-Bellman (HJB) equation, a crucial partial differential equation that characterizes the optimal cost-to-go function. Explore discrete dynamic programming, delve into real-world applications, and understand the inherent limitations of DP, such as the infamous "curse of dimensionality." Prepare to be amazed by "Pontryagin's Maximum Principle," a formidable method for solving optimal control problems, especially those with nonlinear dynamics and constraints. We guide you through the principle's intricacies, showcasing its versatility through numerous examples that demonstrate its power in devising optimal control strategies for a diverse range of systems. Focus is placed on understanding the necessary conditions for optimality derived from the principle. Enter the domain of the "Linear Quadratic Regulator (LQR)," a remarkably applicable optimal control problem. Formulate the problem with precision, understanding the linear system dynamics and the quadratic cost function. Discover the solution, highlighting the vital role of the Riccati equation in determining the optimal control law. This chapter emphasizes the analytical clarity and practical significance of the LQR framework, making it an indispensable tool in your arsenal. Chart your course to control mastery today!
The Calculus Of Variations And Functional Analysis
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Author : L. P. Lebedev
language : en
Publisher: World Scientific
Release Date : 2003
The Calculus Of Variations And Functional Analysis written by L. P. Lebedev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
In this book, Sam helps his goose sisters fly to safety to looking for familiar landforms.
Optimal Control
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Author : Arturo Locatelli
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03
Optimal Control written by Arturo Locatelli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03 with Education categories.
From the reviews: "The style of the book reflects the author’s wish to assist in the effective learning of optimal control by suitable choice of topics, the mathematical level used, and by including numerous illustrated examples. . . .In my view the book suits its function and purpose, in that it gives a student a comprehensive coverage of optimal control in an easy-to-read fashion." —Measurement and Control
Control And Optimal Control Theories With Applications
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Author : D N Burghes
language : en
Publisher: Horwood Publishing
Release Date : 2004-12-15
Control And Optimal Control Theories With Applications written by D N Burghes and has been published by Horwood Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-15 with Computers categories.
This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control theory to varied and important present-day problems, e.g. economic growth, resource depletion, disease epidemics, exploited population, and rocket trajectories. An original feature is the amount of space devoted to the important and fascinating subject of optimal control. The work is divided into two parts. Part one deals with the control of linear time-continuous systems, using both transfer function and state-space methods. The ideas of controllability, observability and minimality are discussed in comprehensible fashion. Part two introduces the calculus of variations, followed by analysis of continuous optimal control problems. Each topic is individually introduced and carefully explained with illustrative examples and exercises at the end of each chapter to help and test the reader's understanding. Solutions are provided at the end of the book. Investigates the many applications of control theory to varied and important present-day problems Deals with the control of linear time-continuous systems, using both transfer function and state-space methods Introduces the calculus of variations, followed by analysis of continuous optimal control problems