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Calculus Of Variations And Optimal Control Theory

Calculus of Variations and Optimal Control Theory PDF
Author: Daniel Liberzon
Publisher: Princeton University Press
Release: 2012
Size: 47.88 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 235
View: 5283

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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

The Calculus Of Variations And Optimal Control

The Calculus of Variations and Optimal Control PDF
Author: George Leitmann
Publisher: Springer Science & Business Media
Release: 2013-06-29
Size: 34.32 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 312
View: 2734

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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

Calculus of Variations and Optimal Control PDF
Author: N. P. Osmolovskii
Publisher: American Mathematical Soc.
Release: 1998-08-18
Size: 68.99 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 372
View: 4081

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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.

A Primer On The Calculus Of Variations And Optimal Control Theory

A Primer on the Calculus of Variations and Optimal Control Theory PDF
Author: Mike Mesterton-Gibbons
Publisher: American Mathematical Soc.
Release: 2009
Size: 57.90 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 252
View: 2169

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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 Theory Of Optimal Control And The Calculus Of Variations

The Theory of Optimal Control and the Calculus of Variations PDF
Author: Rudolf Emil Kalman
Publisher:
Release: 1961*
Size: 76.91 MB
Format: PDF, Docs
Category : Calculus of variations
Languages : en
Pages : 31
View: 5938

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The hamiltonian theory of the calculus of variations is formulated for a wide variety of problems in the theory of control. The hamiltonian function is constructed with the aid of the Minimum Principle, which is the counterpart of the same principle due to Pontryagin. The canonical differential equations of Hamilton are shown to imply Pontryagin's theorem. A number of concrete examples are included. (Author).

Control Theory And The Calculus Of Variations

Control Theory and the Calculus of Variations PDF
Author: A. V. Balakrishnan
Publisher:
Release: 1969
Size: 49.22 MB
Format: PDF, ePub
Category : Calculus
Languages : en
Pages : 422
View: 6933

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Quadratic variational theory; Stochastic functional equations: continuity properties and relation to ordinary equations; Partial regularity theorems for elliptic systems; Strengthening caratheodory's method to apply in control problems; Optimal control problems as mathematical programming in an unorthodox function space; Controlled diffusions under polynomial growth conditions; Separation and support properties of convex sets - a survey; Some non-classical variational problems arising from optimal filter problems; A new existence theorem in the class of piecewise continuous control functions; The epsilon technique - a constructive approach to optimal control; Lagrange multipliers re-visited.

Optimale Steuerung Partieller Differentialgleichungen

Optimale Steuerung partieller Differentialgleichungen PDF
Author: Fredi Tröltzsch
Publisher: Springer-Verlag
Release: 2010-02-21
Size: 19.40 MB
Format: PDF, Mobi
Category : Mathematics
Languages : de
Pages : 311
View: 6067

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Die mathematische Theorie der optimalen Steuerung hat sich im Zusammenhang mit Berechnungen für die Luft- und Raumfahrt schnell zu einem wichtigen und eigenständigen Gebiet der angewandten Mathematik entwickelt. Die optimale Steuerung durch partielle Differentialgleichungen modellierter Prozesse wird eine numerische Herausforderung der Zukunft sein. Im Buch werden entsprechende Grundlagen mit langsam steigendem Schwierigkeitsgrad entwickelt. Es enthält viele Beispiele und eignet sich als Grundlage für Vorlesungen und Seminare. Der Text wurde für die 2. Auflage grundlegend überarbeitet. Die Darstellung der numerischen Methoden orientiert sich stärker an den konkret zu rechnenden Systemen. Neueste Ergebnisse zur maximalen Regularität parabolischer Differentialgleichungen sind eingearbeitet. Lösungshinweise zu den Übungsaufgaben findet der Studierende nun im OnlinePLUS-Service des Verlages.

Constrained Optimization In The Calculus Of Variations And Optimal Control Theory

Constrained Optimization In The Calculus Of Variations and Optimal Control Theory PDF
Author: J Gregory
Publisher: CRC Press
Release: 2018-01-18
Size: 46.99 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 232
View: 1786

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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.