Infinite Horizon Optimal Control In The Discrete Time Framework

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Infinite-Horizon Optimal Control in the Discrete-Time Framework

Joël Blot,Naïla Hayek
Infinite Horizon Optimal Control in the Discrete Time Framework Book PDF

Author : Joël Blot,Naïla Hayek
Publisher : Springer Science & Business Media
Page : 130 pages
File Size : 53,6 Mb
Release : 2013-11-08
Category : Mathematics
ISBN : 9781461490388

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Infinite-Horizon Optimal Control in the Discrete-Time Framework by Joël Blot,Naïla Hayek Pdf

​​​​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.

Discrete-Time Optimal Control and Games on Large Intervals

Alexander J. Zaslavski
Discrete Time Optimal Control and Games on Large Intervals Book PDF

Author : Alexander J. Zaslavski
Publisher : Springer
Page : 398 pages
File Size : 40,9 Mb
Release : 2017-04-03
Category : Mathematics
ISBN : 9783319529325

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Discrete-Time Optimal Control and Games on Large Intervals by Alexander J. Zaslavski Pdf

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.

Advances in Mathematical Economics

Shigeo Kusuoka,Toru Maruyama
Advances in Mathematical Economics Book PDF

Author : Shigeo Kusuoka,Toru Maruyama
Publisher : Springer
Page : 162 pages
File Size : 43,9 Mb
Release : 2017-06-16
Category : Mathematics
ISBN : 9789811041457

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Advances in Mathematical Economics by Shigeo Kusuoka,Toru Maruyama Pdf

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Control Systems and Mathematical Methods in Economics

Gustav Feichtinger,Raimund M. Kovacevic,Gernot Tragler
Control Systems and Mathematical Methods in Economics Book PDF

Author : Gustav Feichtinger,Raimund M. Kovacevic,Gernot Tragler
Publisher : Springer
Page : 439 pages
File Size : 52,7 Mb
Release : 2018-06-08
Category : Business & Economics
ISBN : 9783319751696

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Control Systems and Mathematical Methods in Economics by Gustav Feichtinger,Raimund M. Kovacevic,Gernot Tragler Pdf

Since the days of Lev Pontryagin and his associates, the discipline of Optimal Control has enjoyed a tremendous upswing – not only in terms of its mathematical foundations, but also with regard to numerous fields of application, which have given rise to highly active research areas. Few scholars, however, have been able to make contributions to both the mathematical developments and the (socio-)economic applications; Vladimir Veliov is one of them. In the course of his scientific career, he has contributed highly influential research on mathematical aspects of Optimal Control Theory, as well as applications in Economics and Operations Research. One of the hallmarks of his research is its impressive breadth. This volume, published on the occasion of his 65th birthday, accurately reflects that diversity. The mathematical aspects covered include stability theory for difference inclusions, metric regularity, generalized duality theory, the Bolza problem from a functional analytic perspective, and fractional calculus. In turn, the book explores various applications of control theory, such as population dynamics, population economics, epidemiology, optimal growth theory, resource and energy economics, environmental management, and climate change. Further topics include optimal liquidity, dynamics of the firm, and wealth inequality.

Optimal Control Problems Arising in Mathematical Economics

Alexander J. Zaslavski
Optimal Control Problems Arising in Mathematical Economics Book PDF

Author : Alexander J. Zaslavski
Publisher : Springer Nature
Page : 387 pages
File Size : 47,5 Mb
Release : 2022-06-28
Category : Mathematics
ISBN : 9789811692987

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Optimal Control Problems Arising in Mathematical Economics by Alexander J. Zaslavski Pdf

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.

Mathematical Modelling and Optimization of Engineering Problems

J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Mathematical Modelling and Optimization of Engineering Problems Book PDF

Author : J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Publisher : Springer Nature
Page : 204 pages
File Size : 40,8 Mb
Release : 2020-02-12
Category : Mathematics
ISBN : 9783030370626

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Mathematical Modelling and Optimization of Engineering Problems by J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu Pdf

This book presents recent developments in modelling and optimization of engineering systems and the use of advanced mathematical methods for solving complex real-world problems. It provides recent theoretical developments and new techniques based on control, optimization theory, mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena including latest technologies such as additive manufacturing. Specific topics covered in detail include combinatorial optimization, flow and heat transfer, mathematical modelling, energy storage and management policy, artificial intelligence, optimal control, modelling and optimization of manufacturing systems.

Turnpike Phenomenon and Infinite Horizon Optimal Control

Alexander J. Zaslavski
Turnpike Phenomenon and Infinite Horizon Optimal Control Book PDF

Author : Alexander J. Zaslavski
Publisher : Springer
Page : 370 pages
File Size : 55,6 Mb
Release : 2014-09-04
Category : Mathematics
ISBN : 9783319088280

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Turnpike Phenomenon and Infinite Horizon Optimal Control by Alexander J. Zaslavski Pdf

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.

Turnpike Conditions in Infinite Dimensional Optimal Control

Alexander J. Zaslavski
Turnpike Conditions in Infinite Dimensional Optimal Control Book PDF

Author : Alexander J. Zaslavski
Publisher : Springer
Page : 570 pages
File Size : 50,8 Mb
Release : 2019-07-23
Category : Mathematics
ISBN : 9783030201784

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Turnpike Conditions in Infinite Dimensional Optimal Control by Alexander J. Zaslavski Pdf

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.

Infinite Horizon Optimal Control

Dean A. Carlson,Alain Haurie
Infinite Horizon Optimal Control Book PDF

Author : Dean A. Carlson,Alain Haurie
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 47,5 Mb
Release : 2013-06-29
Category : Business & Economics
ISBN : 9783662025291

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Infinite Horizon Optimal Control by Dean A. Carlson,Alain Haurie Pdf

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.

Numerical Control: Part A

Anonim
Numerical Control Part A Book PDF

Author : Anonim
Publisher : Elsevier
Page : 596 pages
File Size : 49,6 Mb
Release : 2022-02-15
Category : Mathematics
ISBN : 9780323853392

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Numerical Control: Part A by Anonim Pdf

Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control

Turnpike Theory of Continuous-Time Linear Optimal Control Problems

Alexander J. Zaslavski
Turnpike Theory of Continuous Time Linear Optimal Control Problems Book PDF

Author : Alexander J. Zaslavski
Publisher : Springer
Page : 296 pages
File Size : 43,9 Mb
Release : 2015-07-01
Category : Mathematics
ISBN : 9783319191416

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Turnpike Theory of Continuous-Time Linear Optimal Control Problems by Alexander J. Zaslavski Pdf

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.

Turnpike Theory for the Robinson–Solow–Srinivasan Model

Alexander J. Zaslavski
Turnpike Theory for the Robinson Solow Srinivasan Model Book PDF

Author : Alexander J. Zaslavski
Publisher : Springer Nature
Page : 448 pages
File Size : 45,6 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9783030603076

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Turnpike Theory for the Robinson–Solow–Srinivasan Model by Alexander J. Zaslavski Pdf

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 Problems Arising in Forest Management

Alexander J. Zaslavski
Optimal Control Problems Arising in Forest Management Book PDF

Author : Alexander J. Zaslavski
Publisher : Springer
Page : 136 pages
File Size : 46,5 Mb
Release : 2019-08-16
Category : Mathematics
ISBN : 9783030235871

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Optimal Control Problems Arising in Forest Management by Alexander J. Zaslavski Pdf

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.

Nonlinear Analysis and Optimization

Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski
Nonlinear Analysis and Optimization Book PDF

Author : Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski
Publisher : American Mathematical Soc.
Page : 320 pages
File Size : 53,8 Mb
Release : 2016-02-26
Category : Game theory, economics, social and behavioral sciences
ISBN : 9781470417369

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Nonlinear Analysis and Optimization by Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski Pdf

This volume contains the proceedings of the IMU/AMS Special Session on Nonlinear Analysis and Optimization, held from June 16-19, 2014, at the Second Joint International Meeting of the Israel Mathematical Union (IMU) and the American Mathematical Society (AMS), Bar-Ilan and Tel-Aviv Universities, Israel, and the Workshop on Nonlinear Analysis and Optimization, held on June 12, 2014, at the Technion-Israel Institute of Technology. The papers in this volume cover many different topics in Nonlinear Analysis and Optimization, including: Taylor domination property for analytic functions in the complex disk, mappings with upper integral bounds for p -moduli, multiple Fourier transforms and trigonometric series in line with Hardy's variation, finite-parameter feedback control for stabilizing damped nonlinear wave equations, implicit Euler approximation and optimization of one-sided Lipschitz differential inclusions, Bolza variational problems with extended-valued integrands on large intervals, first order singular variational problem with nonconvex cost, gradient and extragradient methods for the elasticity imaging inverse problem, discrete approximations of the entropy functional for probability measures on the plane, optimal irrigation scheduling for wheat production, existence of a fixed point of nonexpansive mappings in uniformly convex Banach spaces, strong convergence properties of m-accretive bounded operators, the Reich-Simons convex analytic inequality, nonlinear input-output equilibrium, differential linear-quadratic Nash games with mixed state-control constraints, and excessive revenue models of competitive markets.

Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory

Timothy L. Molloy,Jairo Inga Charaja,Sören Hohmann,Tristan Perez
Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory Book PDF

Author : Timothy L. Molloy,Jairo Inga Charaja,Sören Hohmann,Tristan Perez
Publisher : Springer Nature
Page : 278 pages
File Size : 50,8 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030933173

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Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory by Timothy L. Molloy,Jairo Inga Charaja,Sören Hohmann,Tristan Perez Pdf

This book presents a novel unified treatment of inverse problems in optimal control and noncooperative dynamic game theory. It provides readers with fundamental tools for the development of practical algorithms to solve inverse problems in control, robotics, biology, and economics. The treatment involves the application of Pontryagin's minimum principle to a variety of inverse problems and proposes algorithms founded on the elegance of dynamic optimization theory. There is a balanced emphasis between fundamental theoretical questions and practical matters. The text begins by providing an introduction and background to its topics. It then discusses discrete-time and continuous-time inverse optimal control. The focus moves on to differential and dynamic games and the book is completed by consideration of relevant applications. The algorithms and theoretical results developed in Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory provide new insights into information requirements for solving inverse problems, including the structure, quantity, and types of state and control data. These insights have significant practical consequences in the design of technologies seeking to exploit inverse techniques such as collaborative robots, driver-assistance technologies, and autonomous systems. The book will therefore be of interest to researchers, engineers, and postgraduate students in several disciplines within the area of control and robotics.