Fundamental Concepts and Problems of Optimal Control Theory
Author | : Laurence Chisholm Young |
Publisher | : |
Total Pages | : 50 |
Release | : 1970 |
Genre | : Control theory |
ISBN | : |
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Author | : Laurence Chisholm Young |
Publisher | : |
Total Pages | : 50 |
Release | : 1970 |
Genre | : Control theory |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 0 |
Release | : 1970 |
Genre | : |
ISBN | : |
The report contains a series of three introductory lectures, and one somewhat specialized lecture, on the mathematical theory of optimization for those control problems which concern systems with a continuously varying time. (Author).
Author | : R. Gamkrelidze |
Publisher | : Springer Science & Business Media |
Total Pages | : 180 |
Release | : 2013-03-09 |
Genre | : Science |
ISBN | : 1468473980 |
In the late 1950's, the group of Soviet mathematicians consisting of L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko made fundamental contributions to optimal control theory. Much of their work was collected in their monograph, The Mathematical Theory of Optimal Processes. Subsequently, Professor Gamkrelidze made further important contributions to the theory of necessary conditions for problems of optimal control and general optimization problems. In the present monograph, Professor Gamkrelidze presents his current view of the fundamentals of optimal control theory. It is intended for use in a one-semester graduate course or advanced undergraduate course. We are now making these ideas available in English to all those interested in optimal control theory. West Lafayette, Indiana, USA Leonard D. Berkovitz Translation Editor Vll Preface This book is based on lectures I gave at the Tbilisi State University during the fall of 1974. It contains, in essence, the principles of general control theory and proofs of the maximum principle and basic existence theorems of optimal control theory. Although the proofs of the basic theorems presented here are far from being the shortest, I think they are fully justified from the conceptual view point. In any case, the notions we introduce and the methods developed have one unquestionable advantage -they are constantly used throughout control theory, and not only for the proofs of the theorems presented in this book.
Author | : Laurence Chisholm Young |
Publisher | : |
Total Pages | : 79 |
Release | : 1970 |
Genre | : Control theory |
ISBN | : |
Author | : Donald E. Kirk |
Publisher | : Courier Corporation |
Total Pages | : 466 |
Release | : 2012-04-26 |
Genre | : Technology & Engineering |
ISBN | : 0486135071 |
Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.
Author | : Suresh P. Sethi |
Publisher | : Taylor & Francis US |
Total Pages | : 536 |
Release | : 2006 |
Genre | : Business & Economics |
ISBN | : 9780387280929 |
Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.
Author | : David G. Hull |
Publisher | : Springer Science & Business Media |
Total Pages | : 402 |
Release | : 2013-03-09 |
Genre | : Technology & Engineering |
ISBN | : 1475741804 |
The published material represents the outgrowth of teaching analytical optimization to aerospace engineering graduate students. To make the material available to the widest audience, the prerequisites are limited to calculus and differential equations. It is also a book about the mathematical aspects of optimal control theory. It was developed in an engineering environment from material learned by the author while applying it to the solution of engineering problems. One goal of the book is to help engineering graduate students learn the fundamentals which are needed to apply the methods to engineering problems. The examples are from geometry and elementary dynamical systems so that they can be understood by all engineering students. Another goal of this text is to unify optimization by using the differential of calculus to create the Taylor series expansions needed to derive the optimality conditions of optimal control theory.
Author | : Thomas A. Weber |
Publisher | : MIT Press |
Total Pages | : 387 |
Release | : 2011-09-30 |
Genre | : Business & Economics |
ISBN | : 0262015730 |
A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.
Author | : Jason L. Speyer |
Publisher | : SIAM |
Total Pages | : 316 |
Release | : 2010-05-13 |
Genre | : Mathematics |
ISBN | : 0898716942 |
A rigorous introduction to optimal control theory, which will enable engineers and scientists to put the theory into practice.
Author | : John T. Betts |
Publisher | : SIAM |
Total Pages | : 442 |
Release | : 2010-01-01 |
Genre | : Mathematics |
ISBN | : 0898716888 |
A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.