Constrained Optimization In The Calculus Of Variations And Optimal Control Theory

Author : J Gregory
Publisher : CRC Press
Page : 232 pages
File Size : 45,6 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.

Author : John Gregory,C. Lin
Publisher : Springer
Page : 217 pages
File Size : 42,6 Mb
Release : 1992-05-31
Category : Computers
ISBN : 0412742306

Get Book

Constrained Optimization in the Calculus of Variations and Optimal Control Theory by John Gregory,C. Lin Pdf

A major problem in current applied mathematics is the lack of efficient and accurate techniques to solve optimization problems in the calculus of variations and optimal control theory. This is surprising since problems occur throughout many areas of applied mathematics, engineering, physical sciences, economics, and biomedicine. For instance, these techniques are used to solve rocket trajectory problems, current flow problems in electronics manufacturing, and financial risk problems in investing. The authors have written a unique book to remedy this problem. The first half of the book contains classical material in the field, the second half unique theoretical and numerical methods for constrained problems.

Author : John Gregory,C. Lin
Publisher : Springer
Page : 217 pages
File Size : 42,7 Mb
Release : 2012-09-17
Category : Computers
ISBN : 9401052956

Get Book

Constrained Optimization in the Calculus of Variations and Optimal Control Theory by John Gregory,C. Lin Pdf

A major problem in current applied mathematics is the lack of efficient and accurate techniques to solve optimization problems in the calculus of variations and optimal control theory. This is surprising since problems occur throughout many areas of applied mathematics, engineering, physical sciences, economics, and biomedicine. For instance, these techniques are used to solve rocket trajectory problems, current flow problems in electronics manufacturing, and financial risk problems in investing. The authors have written a unique book to remedy this problem. The first half of the book contains classical material in the field, the second half unique theoretical and numerical methods for constrained problems.

Author : N. P. Osmolovskii
Publisher : American Mathematical Soc.
Page : 392 pages
File Size : 47,8 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.

Author : Mike Mesterton-Gibbons
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 44,7 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.

Author : George Leitmann
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 44,5 Mb
Release : 1981-05-31
Category : Mathematics
ISBN : 0306407078

Get Book

The Calculus of Variations and Optimal Control by George Leitmann Pdf

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.

Author : Morton I. Kamien,Nancy L. Schwartz
Publisher : Courier Corporation
Page : 402 pages
File Size : 40,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9780486310282

Get Book

Dynamic Optimization, Second Edition by Morton I. Kamien,Nancy L. Schwartz Pdf

Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

Author : Bulirsch,Miele,Stoer,Well
Publisher : Birkhäuser
Page : 352 pages
File Size : 52,8 Mb
Release : 2013-03-08
Category : Science
ISBN : 9783034875394

Get Book

Optimal Control by Bulirsch,Miele,Stoer,Well Pdf

"Optimal Control" reports on new theoretical and practical advances essential for analysing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations. New necessary and sufficient conditions for optimality are given. Recent advances in numerical methods are discussed. These have been achieved through new techniques for solving large-sized nonlinear programs with sparse Hessians, and through a combination of direct and indirect methods for solving the multipoint boundary value problem. The book also focuses on the construction of feedback controls for nonlinear systems and highlights advances in the theory of problems with uncertainty. Decomposition methods of nonlinear systems and new techniques for constructing feedback controls for state- and control constrained linear quadratic systems are presented. The book offers solutions to many complex practical optimal control problems.

Author : Daniel Liberzon
Publisher : Princeton University Press
Page : 254 pages
File Size : 46,5 Mb
Release : 2011-12-19
Category : Mathematics
ISBN : 9781400842643

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

Author : Magnus Rudolph Hestenes
Publisher : Unknown
Page : 432 pages
File Size : 50,8 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015004496074

Get Book

Calculus of Variations and Optimal Control Theory by Magnus Rudolph Hestenes Pdf

Author : Daniel Liberzon
Publisher : Unknown
Page : 256 pages
File Size : 42,7 Mb
Release : 2012-01-01
Category : Calculus of variations
ISBN : 0691155135

Get Book

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

Author : Vadim Krotov
Publisher : CRC Press
Page : 410 pages
File Size : 47,7 Mb
Release : 1995-10-13
Category : Mathematics
ISBN : 0824793293

Get Book

Global Methods in Optimal Control Theory by Vadim Krotov Pdf

This work describes all basic equaitons and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control. Subjects addressed include developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications.

Author : Daniel Léonard,Ngo van Long
Publisher : Cambridge University Press
Page : 368 pages
File Size : 49,9 Mb
Release : 1992-01-31
Category : Business & Economics
ISBN : 9781107717176

Get Book

Optimal Control Theory and Static Optimization in Economics by Daniel Léonard,Ngo van Long Pdf

Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Economic intuitions are emphasized, and examples and problem sets covering a wide range of applications in economics are provided to assist in the learning process. Theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with simple formulations and progressing to advanced topics such as control parameters, jumps in state variables, and bounded state space. For greater economy and elegance, optimal control theory is introduced directly, without recourse to the calculus of variations. The connection with the latter and with dynamic programming is explained in a separate chapter. A second purpose of the book is to draw the parallel between optimal control theory and static optimization. Chapter 1 provides an extensive treatment of constrained and unconstrained maximization, with emphasis on economic insight and applications. Starting from basic concepts, it derives and explains important results, including the envelope theorem and the method of comparative statics. This chapter may be used for a course in static optimization. The book is largely self-contained. No previous knowledge of differential equations is required.

Author : Donald A. Pierre
Publisher : Courier Corporation
Page : 640 pages
File Size : 55,8 Mb
Release : 2012-07-12
Category : Mathematics
ISBN : 9780486136950

Get Book

Optimization Theory with Applications by Donald A. Pierre Pdf

Broad-spectrum approach to important topic. Explores the classic theory of minima and maxima, classical calculus of variations, simplex technique and linear programming, optimality and dynamic programming, more. 1969 edition.

Author : Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 52,7 Mb
Release : 2010-08-05
Category : Mathematics
ISBN : 9780387894966

Get Book

Optimization and Optimal Control by Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj Pdf

Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. “Optimization and Optimal Control: Theory and Applications” brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.