Calculus of Variations and Optimal Control Theory

A Concise Introduction

Author: Daniel Liberzon

Publisher: Princeton University Press

ISBN: 0691151873

Category: Mathematics

Page: 235

View: 7476

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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 and Optimal Control Theory - A Concise Introduction Instructor′s Manual

Author: Daniel Liberzon

Publisher: N.A

ISBN: 9780691155135

Category: Calculus of variations

Page: 256

View: 2220

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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

Hybrid Systems, Optimal Control and Hybrid Vehicles

Theory, Methods and Applications

Author: Thomas J. Böhme,Benjamin Frank

Publisher: Springer

ISBN: 3319513176

Category: Technology & Engineering

Page: 530

View: 5678

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This book assembles new methods showing the automotive engineer for the first time how hybrid vehicle configurations can be modeled as systems with discrete and continuous controls. These hybrid systems describe naturally and compactly the networks of embedded systems which use elements such as integrators, hysteresis, state-machines and logical rules to describe the evolution of continuous and discrete dynamics and arise inevitably when modeling hybrid electric vehicles. They can throw light on systems which may otherwise be too complex or recondite. Hybrid Systems, Optimal Control and Hybrid Vehicles shows the reader how to formulate and solve control problems which satisfy multiple objectives which may be arbitrary and complex with contradictory influences on fuel consumption, emissions and drivability. The text introduces industrial engineers, postgraduates and researchers to the theory of hybrid optimal control problems. A series of novel algorithmic developments provides tools for solving engineering problems of growing complexity in the field of hybrid vehicles. Important topics of real relevance rarely found in text books and research publications—switching costs, sensitivity of discrete decisions and there impact on fuel savings, etc.—are discussed and supported with practical applications. These demonstrate the contribution of optimal hybrid control in predictive energy management, advanced powertrain calibration, and the optimization of vehicle configuration with respect to fuel economy, lowest emissions and smoothest drivability. Numerical issues such as computing resources, simplifications and stability are treated to enable readers to assess such complex systems. To help industrial engineers and managers with project decision-making, solutions for many important problems in hybrid vehicle control are provided in terms of requirements, benefits and risks.

Optimization and Approximation

Author: Pablo Pedregal

Publisher: Springer

ISBN: 3319648438

Category: Mathematics

Page: 254

View: 7741

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This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

Introduction to the Calculus of Variations and Control with Modern Applications

Author: John A. Burns

Publisher: CRC Press

ISBN: 146657139X

Category: Mathematics

Page: 562

View: 7496

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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 and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.

The Calculus of Variations and Functional Analysis

With Optimal Control and Applications in Mechanics

Author: Leonid P Lebedev,Michael J Cloud

Publisher: World Scientific

ISBN: 9814485179

Category: Technology & Engineering

Page: 436

View: 5155

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' 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. Contents:Basic Calculus of VariationsElements of Optimal Control TheoryFunctional AnalysisSome Applications in Mechanics Readership: Graduate students, academics and practitioners in engineering, applied physics and applied mathematics. Keywords:Calculus of Variations;Optimal Control;Functional Analysis;Boundary Value ProblemsReviews:“I recommend this book to all engineers who are interested in modern mathematics. Moreover, mathematicians can learn a lot about direct applications of mathematical theory in mechanics.”Arnd Rösch Technical University of Berlin “The present book is lucid, well-connected, and concise. The material has been carefully chosen. Throughout the book, the authors lay stress on central ideas as they present one powerful mathematical tool after another. The reader is thus prepared not only to apply the material to his or her own work, but also to delve further into the literature if desired.”Technische Mechanik “This book is a significant contribution to the process of successful preparation of engineering students. It is also a good methodical foundation for engineers and lecturers in their work.”Zentralblatt MATH “This book is a welcome addition to the literature on applications of optimal control to various fields in engineering such as mechanics. It is well-written with exercises at the end of each chapter including the hints for the exercises.”International Journal of Robust and Nonlinear Control '

The Calculus of Variations and Functional Analysis

With Optimal Control and Applications in Mechanics

Author: L. P. Lebedev,Michael J. Cloud

Publisher: World Scientific

ISBN: 9812385819

Category: Mathematics

Page: 420

View: 6014

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

Optimal Control of Nonlinear Processes

With Applications in Drugs, Corruption, and Terror

Author: Dieter Grass,Jonathan P. Caulkins,Gustav Feichtinger,Gernot Tragler,Doris A. Behrens

Publisher: Springer Science & Business Media

ISBN: 3540776478

Category: Business & Economics

Page: 552

View: 365

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Dynamic optimization is rocket science – and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in space flight, but also in emerging social applications such as the control of drugs, corruption, and terror. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. The authors celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding. The rich theory explored here is complemented by numerical methods available through a companion web site.

Einführung in die Geometrie und Topologie

Author: Werner Ballmann

Publisher: Springer-Verlag

ISBN: 3034809018

Category: Mathematics

Page: 162

View: 570

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Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.

Glück, Logik und Bluff

Mathematik in Spiel — Methoden, Ergebnisse und Grenzen

Author: Jörg Bewersdorff

Publisher: Springer-Verlag

ISBN: 3663108139

Category: Mathematics

Page: 357

View: 3495

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Glück, Logik und Bluff - drei Begriffe, die abhängig vom Charakter eines Gesellschaftsspieles Wege zum Gewinn weisen. Eng damit verbunden sind drei mathematische Theorien: Die Wahrscheinlichkeitsrechung erlaubt es, die Gewinnchancen in Glücksspielen zu kalkulieren. Von Algorithmen, wie sie auch Schachcomputern zugrundeliegen, handelt die Theorie der kombinatorischen Spiele. Ganz andere Optimierungsansätze, nämlich solche aus der mathematischen Spieltheorie, sind gefragt, wenn Mitspieler wie bei Kartenspielen unterschiedliche Informationsstände über den erreichten Spielstand haben. Anhand vielfältiger (Bei-) Spiele werden Teile der drei Theorien vorgestellt.

Wahrscheinlichkeitstheorie und Stochastische Prozesse

Author: Michael Mürmann

Publisher: Springer-Verlag

ISBN: 364238160X

Category: Mathematics

Page: 428

View: 7946

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Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

Optimal Control Theory

Author: L.D. Berkovitz

Publisher: Springer Science & Business Media

ISBN: 1475760973

Category: Mathematics

Page: 306

View: 3005

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This book is an introduction to the mathematical theory of optimal control of processes governed by ordinary differential eq- tions. It is intended for students and professionals in mathematics and in areas of application who want a broad, yet relatively deep, concise and coherent introduction to the subject and to its relati- ship with applications. In order to accommodate a range of mathema- cal interests and backgrounds among readers, the material is arranged so that the more advanced mathematical sections can be omitted wi- out loss of continuity. For readers primarily interested in appli- tions a recommended minimum course consists of Chapter I, the sections of Chapters II, III, and IV so recommended in the introductory sec tions of those chapters, and all of Chapter V. The introductory sec tion of each chapter should further guide the individual reader toward material that is of interest to him. A reader who has had a good course in advanced calculus should be able to understand the defini tions and statements of the theorems and should be able to follow a substantial portion of the mathematical development. The entire book can be read by someone familiar with the basic aspects of Lebesque integration and functional analysis. For the reader who wishes to find out more about applications we recommend references [2], [13], [33], [35], and [50], of the Bibliography at the end of the book.

Mathematik für Ökonomen

Grundlagen, Methoden und Anwendungen

Author: Alpha C. Chiang,Kevin Wainwright,Harald Nitsch

Publisher: Vahlen

ISBN: 3800645122

Category: Business & Economics

Page: 476

View: 903

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Klar und verständlich: Mathematik für Ökonomen. Für viele Studierende der BWL und VWL hat die Mathematik eine ähnliche Anziehungskraft wie bittere Medizin notwendig, aber extrem unangenehm. Das muss nicht sein. Mit diesem Buch gelingt es jedem, die Methoden zu erlernen. Anhand konkreter ökonomischer Anwendungen wird die Mathematik sehr anschaulich erklärt. Schnelle Lernerfolge Von der Wiederholung des Abiturwissens bis zum Niveau aktueller ökonomischer Lehrbücher wird Schritt für Schritt vorgegangen und alle wichtigen Bereiche der Mathematik systematisch erklärt. Der Lernerfolg stellt sich schnell ein: die klare und ausführliche Darstellung sowie die graphische Unterstützung machen es möglich.

Bernhard Riemann 1826–1866

Wendepunkte in der Auffassung der Mathematik

Author: Detlef Laugwitz

Publisher: Springer-Verlag

ISBN: 3034889836

Category: Mathematics

Page: 348

View: 1127

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Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."

Mathematical Control Theory

An Introduction

Author: Jerzy Zabczyk

Publisher: Springer Science & Business Media

ISBN: 9780817647339

Category: Science

Page: 260

View: 9626

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Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. "Covers a remarkable number of topics....The book presents a large amount of material very well, and its use is highly recommended." --Bulletin of the AMS