The Infinite Horizon Optimal Control Problem

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Infinite Horizon Optimal Control

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Author : Dean A. Carlson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Infinite Horizon Optimal Control written by Dean A. Carlson 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 2013-06-29 with Business & Economics categories.

This monograph deals with various classes of deterministic continuous time optimal control problems wh ich are defined over unbounded time intervala. For these problems, the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts; referred to here as "overtaking", "weakly overtaking", "agreeable plans", etc. ; have been proposed. The motivation for studying these problems arisee primarily from the economic and biological aciences where models of this nature arise quite naturally since no natural bound can be placed on the time horizon when one considers the evolution of the state of a given economy or species. The reeponsibility for the introduction of this interesting class of problems rests with the economiste who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey who, in his seminal work on a theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a "Lagrange problem with unbounded time interval". The advent of modern control theory, particularly the formulation of the famoue Maximum Principle of Pontryagin, has had a considerable impact on the treatment of these models as well as optimization theory in general.

The Infinite Horizon Optimal Control Problem

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Author : Lynnell Elizabeth Stern
language : en
Publisher:
Release Date : 1980

The Infinite Horizon Optimal Control Problem written by Lynnell Elizabeth Stern and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Control theory categories.

The Infinite Horizon Optimal Control Problem

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Author : J. C. P. Bus
language : nl
Publisher:
Release Date : 1983

The Infinite Horizon Optimal Control Problem written by J. C. P. Bus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.

Infinite Horizon Optimal Control

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Author : Dean A. Carlson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Infinite Horizon Optimal Control written by Dean A. Carlson 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 2012-12-06 with Business & Economics categories.

This monograph deals with various classes of deterministic and stochastic continuous time optimal control problems that are defined over unbounded time intervals. For these problems the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts, referred to here as overtaking optimality, weakly overtaking optimality, agreeable plans, etc. , have been proposed. The motivation for studying these problems arises primarily from the economic and biological sciences where models of this type arise naturally. Indeed, any bound placed on the time hori zon is artificial when one considers the evolution of the state of an economy or species. The responsibility for the introduction of this interesting class of problems rests with the economists who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey [152] who, in his seminal work on the theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a Lagrange problem with unbounded time interval. The advent of modern control theory, particularly the formulation of the famous Maximum Principle of Pontryagin, has had a considerable impact on the treat ment of these models as well as optimization theory in general.

The Infinite Horizon Optimal Control Problem On Manifolds

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Author : J. C. Bus
language : en
Publisher:
Release Date : 1983

The Infinite Horizon Optimal Control Problem On Manifolds written by J. C. Bus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.

Infinite Horizon Optimal Control In The Discrete Time Framework

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Author : Joël Blot
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-08

Infinite Horizon Optimal Control In The Discrete Time Framework written by Joël Blot 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 2013-11-08 with Mathematics categories.

​​​​In this book the authors take a rigorous look at the infinite-horizon discrete-time optimal control theory from the viewpoint of Pontryagin’s principles. Several Pontryagin principles are described which govern systems and various criteria which define the notions of optimality, along with a detailed analysis of how each Pontryagin principle relate to each other. The Pontryagin principle is examined in a stochastic setting and results are given which generalize Pontryagin’s principles to multi-criteria problems. ​Infinite-Horizon Optimal Control in the Discrete-Time Framework is aimed toward researchers and PhD students in various scientific fields such as mathematics, applied mathematics, economics, management, sustainable development (such as, of fisheries and of forests), and Bio-medical sciences who are drawn to infinite-horizon discrete-time optimal control problems.

Variational And Optimal Control Problems On Unbounded Domains

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Author : Gershon Wolansky
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-07-01

Variational And Optimal Control Problems On Unbounded Domains written by Gershon Wolansky 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 2014-07-01 with Mathematics categories.

This volume contains the proceedings of the workshop on Variational and Optimal Control Problems on Unbounded Domains, held in memory of Arie Leizarowitz, from January 9-12, 2012, in Haifa, Israel. The workshop brought together a select group of worldwide experts in optimal control theory and the calculus of variations, working on problems on unbounded domains. The papers in this volume cover many different areas of optimal control and its applications. Topics include needle variations in infinite-horizon optimal control, Lyapunov stability with some extensions, small noise large time asymptotics for the normalized Feynman-Kac semigroup, linear-quadratic optimal control problems with state delays, time-optimal control of wafer stage positioning, second order optimality conditions in optimal control, state and time transformations of infinite horizon problems, turnpike properties of dynamic zero-sum games, and an infinite-horizon variational problem on an infinite strip. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).

Turnpike Theory For The Robinson Solow Srinivasan Model

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2021-01-04

Turnpike Theory For The Robinson Solow Srinivasan Model written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Mathematics categories.

This book is devoted to the study of a class of optimal control problems arising in mathematical economics, related to the Robinson–Solow–Srinivasan (RSS) model. It will be useful for researches interested in the turnpike theory, infinite horizon optimal control and their applications, and mathematical economists. The RSS is a well-known model of economic dynamics that was introduced in the 1960s and as many other models of economic dynamics, the RSS model is determined by an objective function (a utility function) and a set-valued mapping (a technology map). The set-valued map generates a dynamical system whose trajectories are under consideration and the objective function determines an optimality criterion. The goal is to find optimal trajectories of the dynamical system, using the optimality criterion. Chapter 1 discusses turnpike properties for some classes of discrete time optimal control problems. Chapter 2 present the description of the RSS model and discuss its basic properties. Infinite horizon optimal control problems, related to the RSS model are studied in Chapter 3. Turnpike properties for the RSS model are analyzed in Chapter 4. Chapter 5 studies infinite horizon optimal control problems related to the RSS model with a nonconcave utility function. Chapter 6 focuses on infinite horizon optimal control problems with nonautonomous optimality criterions. Chapter 7 contains turnpike results for a class of discrete-time optimal control problems. Chapter 8 discusses the RSS model and compares different optimality criterions. Chapter 9 is devoted to the study of the turnpike properties for the RSS model. In Chapter 10 the one-dimensional autonomous RSS model is considered and the continuous time RSS model is studied in Chapter 11.

Optimal Control Theory

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Author : Suresh P. Sethi
language : en
Publisher: Springer Nature
Release Date : 2022-01-03

Optimal Control Theory written by Suresh P. Sethi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-03 with Business & Economics categories.

This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.

Turnpike Phenomenon And Symmetric Optimization Problems

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2022-04-11

Turnpike Phenomenon And Symmetric Optimization Problems written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-11 with Mathematics categories.

Written by a leading expert in turnpike phenomenon, this book is devoted to the study of symmetric optimization, variational and optimal control problems in infinite dimensional spaces and turnpike properties of their approximate solutions. The book presents a systematic and comprehensive study of general classes of problems in optimization, calculus of variations, and optimal control with symmetric structures from the viewpoint of the turnpike phenomenon. The author establishes generic existence and well-posedness results for optimization problems and individual (not generic) turnpike results for variational and optimal control problems. Rich in impressive theoretical results, the author presents applications to crystallography and discrete dispersive dynamical systems which have prototypes in economic growth theory. This book will be useful for researchers interested in optimal control, calculus of variations turnpike theory and their applications, such as mathematicians, mathematical economists, and researchers in crystallography, to name just a few.