Turnpike Properties In The Calculus Of Variations And Optimal Control
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Turnpike Properties In The Calculus Of Variations And Optimal Control
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-27
Turnpike Properties In The Calculus Of Variations And Optimal Control written by Alexander J. Zaslavski 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 2006-01-27 with Mathematics categories.
This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics. Audience This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics.
Weiterbildungsnormen Der Rztekammern Auf Dem Rechtlichen Pr Fstand
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Author : Gunther Schwerdtfeger
language : en
Publisher:
Release Date : 1989
Weiterbildungsnormen Der Rztekammern Auf Dem Rechtlichen Pr Fstand written by Gunther Schwerdtfeger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Turnpike Phenomenon And Infinite Horizon Optimal Control
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer
Release Date : 2014-09-04
Turnpike Phenomenon And Infinite Horizon Optimal Control written by Alexander J. Zaslavski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-04 with Mathematics categories.
This book is devoted to the study of the turnpike phenomenon and describes the existence of solutions for a large variety of infinite horizon optimal control classes of problems. Chapter 1 provides introductory material on turnpike properties. Chapter 2 studies the turnpike phenomenon for discrete-time optimal control problems. The turnpike properties of autonomous problems with extended-value integrands are studied in Chapter 3. Chapter 4 focuses on large classes of infinite horizon optimal control problems without convexity (concavity) assumptions. In Chapter 5, the turnpike results for a class of dynamic discrete-time two-player zero-sum game are proven. This thorough exposition will be very useful for mathematicians working in the fields of optimal control, the calculus of variations, applied functional analysis and infinite horizon optimization. It may also be used as a primary text in a graduate course in optimal control or as supplementary text for a variety of courses in other disciplines. Researchers in other fields such as economics and game theory, where turnpike properties are well known, will also find this Work valuable.
Optimal Control Problems Arising In Mathematical Economics
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2022-06-28
Optimal Control Problems Arising In Mathematical Economics 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 2022-06-28 with Mathematics categories.
This book is devoted to the study of two large classes of discrete-time optimal control problems arising in mathematical economics. Nonautonomous optimal control problems of the first class are determined by a sequence of objective functions and sequence of constraint maps. They correspond to a general model of economic growth. We are interested in turnpike properties of approximate solutions and in the stability of the turnpike phenomenon under small perturbations of objective functions and constraint maps. The second class of autonomous optimal control problems corresponds to another general class of models of economic dynamics which includes the Robinson–Solow–Srinivasan model as a particular case. In Chap. 1 we discuss turnpike properties for a large class of discrete-time optimal control problems studied in the literature and for the Robinson–Solow–Srinivasan model. In Chap. 2 we introduce the first class of optimal control problems and study its turnpike property. This class of problems is also discussed in Chaps. 3–6. In Chap. 3 we study the stability of the turnpike phenomenon under small perturbations of the objective functions. Analogous results for problems with discounting are considered in Chap. 4. In Chap. 5 we study the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. Analogous results for problems with discounting are established in Chap. 6. The results of Chaps. 5 and 6 are new. The second class of problems is studied in Chaps. 7–9. In Chap. 7 we study the turnpike properties. The stability of the turnpike phenomenon under small perturbations of the objective functions is established in Chap. 8. In Chap. 9 we establish the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. The results of Chaps. 8 and 9 are new. In Chap. 10 we study optimal control problems related to a model of knowledge-based endogenous economic growth and show the existence of trajectories of unbounded economic growth and provide estimates for the growth rate.
Stability Of The Turnpike Phenomenon In Discrete Time Optimal Control Problems
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer
Release Date : 2014-08-20
Stability Of The Turnpike Phenomenon In Discrete Time Optimal Control Problems written by Alexander J. Zaslavski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-20 with Mathematics categories.
The structure of approximate solutions of autonomous discrete-time optimal control problems and individual turnpike results for optimal control problems without convexity (concavity) assumptions are examined in this book. In particular, the book focuses on the properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals; these results apply to the so-called turnpike property of the optimal control problems. By encompassing the so-called turnpike property the approximate solutions of the problems are determined primarily by the objective function and are fundamentally independent of the choice of interval and endpoint conditions, except in regions close to the endpoints. This book also explores the turnpike phenomenon for two large classes of autonomous optimal control problems. It is illustrated that the turnpike phenomenon is stable for an optimal control problem if the corresponding infinite horizon optimal control problem possesses an asymptotic turnpike property. If an optimal control problem belonging to the first class possesses the turnpike property, then the turnpike is a singleton (unit set). The stability of the turnpike property under small perturbations of an objective function and of a constraint map is established. For the second class of problems where the turnpike phenomenon is not necessarily a singleton the stability of the turnpike property under small perturbations of an objective function is established. Containing solutions of difficult problems in optimal control and presenting new approaches, techniques and methods this book is of interest for mathematicians working in optimal control and the calculus of variations. It also can be useful in preparation courses for graduate students.
Nonconvex Optimal Control And Variational Problems
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-12
Nonconvex Optimal Control And Variational Problems written by Alexander J. Zaslavski 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 2013-06-12 with Mathematics categories.
Nonconvex Optimal Control and Variational Problems is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems. Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with “good” functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author. This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community.
Optimal Control Problems Arising In Forest Management
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer
Release Date : 2019-08-16
Optimal Control Problems Arising In Forest Management written by Alexander J. Zaslavski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with Mathematics categories.
This book is devoted to the study of optimal control problems arising in forest management, an important and fascinating topic in mathematical economics studied by many researchers over the years. The volume studies the forest management problem by analyzing a class of optimal control problems that contains it and showing the existence of optimal solutions over infinite horizon. It also studies the structure of approximate solutions on finite intervals and their turnpike properties, as well as the stability of the turnpike phenomenon and the structure of approximate solutions on finite intervals in the regions close to the end points. The book is intended for mathematicians interested in the optimization theory, optimal control and their applications to the economic theory.
Turnpike Phenomenon In Metric Spaces
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2023-04-17
Turnpike Phenomenon In Metric Spaces 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 2023-04-17 with Mathematics categories.
This book is devoted to the study of the turnpike phenomenon arising in optimal control theory. Special focus is placed on Turnpike results, in sufficient and necessary conditions for the turnpike phenomenon and in its stability under small perturbations of objective functions. The most important feature of this book is that it develops a large, general class of optimal control problems in metric space. Additional value is in the provision of solutions to a number of difficult and interesting problems in optimal control theory in metric spaces. Mathematicians working in optimal control, optimization, and experts in applications of optimal control to economics and engineering, will find this book particularly useful. All main results obtained in the book are new. The monograph contains nine chapters. Chapter 1 is an introduction. Chapter 2 discusses Banach space valued functions, set-valued mappings in infinite dimensional spaces, and related continuous-time dynamical systems. Some convergence results are obtained. In Chapter 3, a discrete-time dynamical system with a Lyapunov function in a metric space induced by a set-valued mapping, is studied. Chapter 4 is devoted to the study of a class of continuous-time dynamical systems, an analog of the class of discrete-time dynamical systems considered in Chapter 3. Chapter 5 develops a turnpike theory for a class of general dynamical systems in a metric space with a Lyapunov function. Chapter 6 contains a study of the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of half-axis in metric spaces, which are not necessarily compact. Chapter 7 contains preliminaries which are needed in order to study turnpike properties of infinite-dimensional optimal control problems. In Chapter 8, sufficient and necessary conditions for the turnpike phenomenon for continuous-time optimal control problems on subintervals of the half-axis in metric spaces, is established. In Chapter 9, the examination continues of the turnpike phenomenon for the continuous-time optimal control problems on subintervals of half-axis in metric spaces discussed in Chapter 8.
Turnpike Theory Of Continuous Time Linear Optimal Control Problems
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer
Release Date : 2015-07-01
Turnpike Theory Of Continuous Time Linear Optimal Control Problems written by Alexander J. Zaslavski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-01 with Mathematics categories.
Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous convex smooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integrands.
Combined Scheduling And Control
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Author : John D. Hedengren
language : en
Publisher: MDPI
Release Date : 2018-04-13
Combined Scheduling And Control written by John D. Hedengren and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-13 with Technology & Engineering categories.
This book is a printed edition of the Special Issue "Combined Scheduling and Control" that was published in Processes