Download or read book Turnpike Properties in the Calculus of Variations and Optimal Control written by Alexander J. Zaslavski and published by Springer Science & Business Media. This book was released on 2006-01-27 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Weiterbildungsnormen der rztekammern auf dem rechtlichen Pr fstand written by Gunther Schwerdtfeger and published by . This book was released on 1989 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Turnpike Phenomenon and Infinite Horizon Optimal Control written by Alexander J. Zaslavski and published by Springer. This book was released on 2014-09-04 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Turnpike Theory of Continuous Time Linear Optimal Control Problems written by Alexander J. Zaslavski and published by Springer. This book was released on 2015-07-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Turnpike Phenomenon and Symmetric Optimization Problems written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2022-04-11 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonconvex Optimal Control and Variational Problems written by Alexander J. Zaslavski and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stability of the Turnpike Phenomenon in Discrete Time Optimal Control Problems written by Alexander J. Zaslavski and published by Springer. This book was released on 2014-08-20 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Turnpike Conditions in Infinite Dimensional Optimal Control written by Alexander J. Zaslavski and published by Springer. This book was released on 2019-07-23 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces. The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved and the numerous illustrative examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces. Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results.

Download or read book Optimal Control Problems Arising in Mathematical Economics written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2022-06-28 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Structure of Approximate Solutions of Optimal Control Problems written by Alexander J. Zaslavski and published by Springer Science & Business Media. This book was released on 2013-08-04 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title examines the structure of approximate solutions of optimal control problems considered on subintervals of a real line. Specifically at the properties of approximate solutions which are independent of the length of the interval. The results illustrated in this book look into the so-called turnpike property of optimal control problems. The author generalizes the results of the turnpike property by considering a class of optimal control problems which is identified with the corresponding complete metric space of objective functions. This establishes the turnpike property for any element in a set that is in a countable intersection which is open everywhere dense sets in the space of integrands; meaning that the turnpike property holds for most optimal control problems. Mathematicians working in optimal control and the calculus of variations and graduate students will find this book useful and valuable due to its presentation of solutions to a number of difficult problems in optimal control and presentation of new approaches, techniques and methods.

Download or read book Combined Scheduling and Control written by John D. Hedengren and published by MDPI. This book was released on 2018-04-13 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Combined Scheduling and Control" that was published in Processes

Download or read book Discrete Time Optimal Control and Games on Large Intervals written by Alexander J. Zaslavski and published by Springer. This book was released on 2017-04-03 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the structure of approximate solutions of discrete-time optimal control problems and approximate solutions of dynamic discrete-time two-player zero-sum games, this book presents results on properties of approximate solutions in an interval that is independent lengthwise, for all sufficiently large intervals. Results concerning the so-called turnpike property of optimal control problems and zero-sum games in the regions close to the endpoints of the time intervals are the main focus of this book. The description of the structure of approximate solutions on sufficiently large intervals and its stability will interest graduate students and mathematicians in optimal control and game theory, engineering, and economics. This book begins with a brief overview and moves on to analyze the structure of approximate solutions of autonomous nonconcave discrete-time optimal control Lagrange problems.Next the structures of approximate solutions of autonomous discrete-time optimal control problems that are discrete-time analogs of Bolza problems in calculus of variations are studied. The structures of approximate solutions of two-player zero-sum games are analyzed through standard convexity-concavity assumptions. Finally, turnpike properties for approximate solutions in a class of nonautonomic dynamic discrete-time games with convexity-concavity assumptions are examined.

Download or read book Turnpike Phenomenon in Metric Spaces written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2023-04-17 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Calculus of Variations and Optimal Control written by N. P. Osmolovskii and published by American Mathematical Soc.. This book was released on 1998-08-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Optimal Control and the Calculus of Variations written by Enid R. Pinch and published by Oxford University Press. This book was released on 1995 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: A paperback edition of this successful textbook for final year undergraduate mathematicians and control engineering students, this book contains exercises and many worked examples, with complete solutions and hints making it ideal not only as a class textbook but also for individual study. Theintorduction to optimal control begins by considering the problem of minimizing a function of many variables, before moving on to the main subject: the optimal control of systems governed by ordinary differential equations.

Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Lectures on the Calculus of Variations and Optimal Control Theory written by Laurence Chisholm Young and published by American Mathematical Soc.. This book was released on 2000 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and "automatic" existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.