Controlled Markov Processes On The Infinite Planning Horizon

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Discrete-Time Markov Control Processes

Author : Onesimo Hernandez-Lerma
Publisher : Springer Science & Business Media
ISBN 13 : 1461207290
Total Pages : 223 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Discrete-Time Markov Control Processes by : Onesimo Hernandez-Lerma

Download or read book Discrete-Time Markov Control Processes written by Onesimo Hernandez-Lerma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes (MCPs). Interest is mainly confined to MCPs with Borel state and control (or action) spaces, and possibly unbounded costs and noncompact control constraint sets. MCPs are a class of stochastic control problems, also known as Markov decision processes, controlled Markov processes, or stochastic dynamic pro grams; sometimes, particularly when the state space is a countable set, they are also called Markov decision (or controlled Markov) chains. Regardless of the name used, MCPs appear in many fields, for example, engineering, economics, operations research, statistics, renewable and nonrenewable re source management, (control of) epidemics, etc. However, most of the lit erature (say, at least 90%) is concentrated on MCPs for which (a) the state space is a countable set, and/or (b) the costs-per-stage are bounded, and/or (c) the control constraint sets are compact. But curiously enough, the most widely used control model in engineering and economics--namely the LQ (Linear system/Quadratic cost) model-satisfies none of these conditions. Moreover, when dealing with "partially observable" systems) a standard approach is to transform them into equivalent "completely observable" sys tems in a larger state space (in fact, a space of probability measures), which is uncountable even if the original state process is finite-valued.

Markov Processes and Controlled Markov Chains

Author : Zhenting Hou
Publisher : Springer Science & Business Media
ISBN 13 : 146130265X
Total Pages : 501 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Markov Processes and Controlled Markov Chains by : Zhenting Hou

Download or read book Markov Processes and Controlled Markov Chains written by Zhenting Hou and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South American and Asian scholars.

Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems

Author : Xi-Ren Cao
Publisher : Springer Nature
ISBN 13 : 3030418464
Total Pages : 376 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems by : Xi-Ren Cao

Download or read book Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems written by Xi-Ren Cao and published by Springer Nature. This book was released on 2020-05-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.

Selected Topics On Continuous-time Controlled Markov Chains And Markov Games

Author : Tomas Prieto-rumeau
Publisher : World Scientific
ISBN 13 : 1908977639
Total Pages : 292 pages
Book Rating : 4.9/5 (89 download)

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Book Synopsis Selected Topics On Continuous-time Controlled Markov Chains And Markov Games by : Tomas Prieto-rumeau

Download or read book Selected Topics On Continuous-time Controlled Markov Chains And Markov Games written by Tomas Prieto-rumeau and published by World Scientific. This book was released on 2012-03-16 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This book is also concerned with Markov games, where two decision-makers (or players) try to optimize their own objective function. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science, among other areas.An extensive, self-contained, up-to-date analysis of basic optimality criteria (such as discounted and average reward), and advanced optimality criteria (e.g., bias, overtaking, sensitive discount, and Blackwell optimality) is presented. A particular emphasis is made on the application of the results herein: algorithmic and computational issues are discussed, and applications to population models and epidemic processes are shown.This book is addressed to students and researchers in the fields of stochastic control and stochastic games. Moreover, it could be of interest also to undergraduate and beginning graduate students because the reader is not supposed to have a high mathematical background: a working knowledge of calculus, linear algebra, probability, and continuous-time Markov chains should suffice to understand the contents of the book.

Further Topics on Discrete-Time Markov Control Processes

Author : Onesimo Hernandez-Lerma
Publisher : Springer Science & Business Media
ISBN 13 : 1461205611
Total Pages : 286 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Further Topics on Discrete-Time Markov Control Processes by : Onesimo Hernandez-Lerma

Download or read book Further Topics on Discrete-Time Markov Control Processes written by Onesimo Hernandez-Lerma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes, the text is mainly confined to MCPs with Borel state and control spaces. Although the book follows on from the author's earlier work, an important feature of this volume is that it is self-contained and can thus be read independently of the first. The control model studied is sufficiently general to include virtually all the usual discrete-time stochastic control models that appear in applications to engineering, economics, mathematical population processes, operations research, and management science.

Handbook of Markov Decision Processes

Author : Eugene A. Feinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461508053
Total Pages : 560 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Handbook of Markov Decision Processes by : Eugene A. Feinberg

Download or read book Handbook of Markov Decision Processes written by Eugene A. Feinberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eugene A. Feinberg Adam Shwartz This volume deals with the theory of Markov Decision Processes (MDPs) and their applications. Each chapter was written by a leading expert in the re spective area. The papers cover major research areas and methodologies, and discuss open questions and future research directions. The papers can be read independently, with the basic notation and concepts ofSection 1.2. Most chap ters should be accessible by graduate or advanced undergraduate students in fields of operations research, electrical engineering, and computer science. 1.1 AN OVERVIEW OF MARKOV DECISION PROCESSES The theory of Markov Decision Processes-also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming-studiessequential optimization ofdiscrete time stochastic systems. The basic object is a discrete-time stochas tic system whose transition mechanism can be controlled over time. Each control policy defines the stochastic process and values of objective functions associated with this process. The goal is to select a "good" control policy. In real life, decisions that humans and computers make on all levels usually have two types ofimpacts: (i) they cost orsavetime, money, or other resources, or they bring revenues, as well as (ii) they have an impact on the future, by influencing the dynamics. In many situations, decisions with the largest immediate profit may not be good in view offuture events. MDPs model this paradigm and provide results on the structure and existence of good policies and on methods for their calculation.

Examples in Markov Decision Processes

Author : A. B. Piunovskiy
Publisher : World Scientific
ISBN 13 : 1848167938
Total Pages : 308 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Examples in Markov Decision Processes by : A. B. Piunovskiy

Download or read book Examples in Markov Decision Processes written by A. B. Piunovskiy and published by World Scientific. This book was released on 2013 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book provides approximately eighty examples illustrating the theory of controlled discrete-time Markov processes. Except for applications of the theory to real-life problems like stock exchange, queues, gambling, optimal search etc, the main attention is paid to counter-intuitive, unexpected properties of optimization problems. Such examples illustrate the importance of conditions imposed in the theorems on Markov Decision Processes. Many of the examples are based upon examples published earlier in journal articles or textbooks while several other examples are new. The aim was to collect them together in one reference book which should be considered as a complement to existing monographs on Markov decision processes. The book is self-contained and unified in presentation. The main theoretical statements and constructions are provided, and particular examples can be read independently of others. Examples in Markov Decision Processes is an essential source of reference for mathematicians and all those who apply the optimal control theory to practical purposes. When studying or using mathematical methods, the researcher must understand what can happen if some of the conditions imposed in rigorous theorems are not satisfied. Many examples confirming the importance of such conditions were published in different journal articles which are often difficult to find. This book brings together examples based upon such sources, along with several new ones. In addition, it indicates the areas where Markov decision processes can be used. Active researchers can refer to this book on applicability of mathematical methods and theorems. It is also suitable reading for graduate and research students where they will better understand the theory.

Optimization, Control, and Applications of Stochastic Systems

Author : Daniel Hernández-Hernández
Publisher : Springer Science & Business Media
ISBN 13 : 0817683372
Total Pages : 331 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Optimization, Control, and Applications of Stochastic Systems by : Daniel Hernández-Hernández

Download or read book Optimization, Control, and Applications of Stochastic Systems written by Daniel Hernández-Hernández and published by Springer Science & Business Media. This book was released on 2012-08-15 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.

Continuous Time Control of Markov Processes on an Arbitrary State Space

Author : Bharat T. Doshi
Publisher :
ISBN 13 :
Total Pages : 492 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Continuous Time Control of Markov Processes on an Arbitrary State Space by : Bharat T. Doshi

Download or read book Continuous Time Control of Markov Processes on an Arbitrary State Space written by Bharat T. Doshi and published by . This book was released on 1974 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies the problem of the control of Markov processes with continuous time parameter and arbitrary state space. The economic criteria used are (a) the expected discounted return over an infinite horizon and (b) the expected average return over an infinite horizon. An extensive theory is available to treat the control problems in which either the time parameter or the state space is discrete. This dissertation extends the available theory to the general case of continuous time parameter and arbitrary state space. An application to the control of the arrival process in an M/G/1 queue is included. (Modified author abstract).

Continuous-Time Markov Decision Processes

Author : Xianping Guo
Publisher : Springer Science & Business Media
ISBN 13 : 3642025471
Total Pages : 240 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Continuous-Time Markov Decision Processes by : Xianping Guo

Download or read book Continuous-Time Markov Decision Processes written by Xianping Guo and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.

Statistics, Probability, and Game Theory

Author : David Blackwell
Publisher : IMS
ISBN 13 : 9780940600423
Total Pages : 428 pages
Book Rating : 4.6/5 (4 download)

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Book Synopsis Statistics, Probability, and Game Theory by : David Blackwell

Download or read book Statistics, Probability, and Game Theory written by David Blackwell and published by IMS. This book was released on 1996 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the 26 papers are research reports on probability, statistics, gambling, game theory, Markov decision processes, set theory, and logic. But they also include reviews on comparing experiments, games of timing, merging opinions, associated memory models, and SPLIF's; historical views of Carnap, von Mises, and the Berkeley Statistics Department; and a brief history, appreciation, and bibliography of Berkeley professor Blackwell. A sampling of titles turns up The Hamiltonian Cycle Problem and Singularly Perturbed Markov Decision Process, A Pathwise Approach to Dynkin Games, The Redistribution of Velocity: Collision and Transformations, Casino Winnings at Blackjack, and Randomness and the Foundations of Probability. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Markov Decision Processes

Author : Martin L. Puterman
Publisher : John Wiley & Sons
ISBN 13 : 1118625870
Total Pages : 544 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Markov Decision Processes by : Martin L. Puterman

Download or read book Markov Decision Processes written by Martin L. Puterman and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "This text is unique in bringing together so many results hitherto found only in part in other texts and papers. . . . The text is fairly self-contained, inclusive of some basic mathematical results needed, and provides a rich diet of examples, applications, and exercises. The bibliographical material at the end of each chapter is excellent, not only from a historical perspective, but because it is valuable for researchers in acquiring a good perspective of the MDP research potential." —Zentralblatt fur Mathematik ". . . it is of great value to advanced-level students, researchers, and professional practitioners of this field to have now a complete volume (with more than 600 pages) devoted to this topic. . . . Markov Decision Processes: Discrete Stochastic Dynamic Programming represents an up-to-date, unified, and rigorous treatment of theoretical and computational aspects of discrete-time Markov decision processes." —Journal of the American Statistical Association

Stochastic Models in Operations Research: Stochastic optimization

Author : Daniel P. Heyman
Publisher : Courier Corporation
ISBN 13 : 9780486432601
Total Pages : 580 pages
Book Rating : 4.4/5 (326 download)

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Book Synopsis Stochastic Models in Operations Research: Stochastic optimization by : Daniel P. Heyman

Download or read book Stochastic Models in Operations Research: Stochastic optimization written by Daniel P. Heyman and published by Courier Corporation. This book was released on 2004-01-01 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set of texts explores the central facts and ideas of stochastic processes, illustrating their use in models based on applied and theoretical investigations. They demonstrate the interdependence of three areas of study that usually receive separate treatments: stochastic processes, operating characteristics of stochastic systems, and stochastic optimization. Comprehensive in its scope, they emphasize the practical importance, intellectual stimulation, and mathematical elegance of stochastic models and are intended primarily as graduate-level texts.

Modern Trends in Controlled Stochastic Processes:

Author : Alexey Piunovskiy
Publisher : Springer Nature
ISBN 13 : 3030769283
Total Pages : 356 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Modern Trends in Controlled Stochastic Processes: by : Alexey Piunovskiy

Download or read book Modern Trends in Controlled Stochastic Processes: written by Alexey Piunovskiy and published by Springer Nature. This book was released on 2021-06-04 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art solution methods and applications of stochastic optimal control. It is a collection of extended papers discussed at the traditional Liverpool workshop on controlled stochastic processes with participants from both the east and the west. New problems are formulated, and progresses of ongoing research are reported. Topics covered in this book include theoretical results and numerical methods for Markov and semi-Markov decision processes, optimal stopping of Markov processes, stochastic games, problems with partial information, optimal filtering, robust control, Q-learning, and self-organizing algorithms. Real-life case studies and applications, e.g., queueing systems, forest management, control of water resources, marketing science, and healthcare, are presented. Scientific researchers and postgraduate students interested in stochastic optimal control,- as well as practitioners will find this book appealing and a valuable reference.

SIAM Journal on Control and Optimization

Author : Society for Industrial and Applied Mathematics
Publisher :
ISBN 13 :
Total Pages : 854 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis SIAM Journal on Control and Optimization by : Society for Industrial and Applied Mathematics

Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 1993 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Continuous-Time Markov Decision Processes

Author : Alexey Piunovskiy
Publisher : Springer Nature
ISBN 13 : 3030549879
Total Pages : 605 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Continuous-Time Markov Decision Processes by : Alexey Piunovskiy

Download or read book Continuous-Time Markov Decision Processes written by Alexey Piunovskiy and published by Springer Nature. This book was released on 2020-11-09 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies. Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth. The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail. Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.

Control of Distributed Parameter Systems

Author : S. P. Banks
Publisher : Elsevier
ISBN 13 : 1483151123
Total Pages : 554 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Control of Distributed Parameter Systems by : S. P. Banks

Download or read book Control of Distributed Parameter Systems written by S. P. Banks and published by Elsevier. This book was released on 2014-05-18 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control of Distributed Parameter Systems covers the proceedings of the Second IFAC Symposium, Coventry, held in Great Britain from June 28 to July 1, 1977. The book focuses on the methodologies, processes, and techniques in the control of distributed parameter systems, including boundary value control, digital transfer matrix, and differential equations. The selection first discusses the asymptotic methods in the optimal control of distributed systems; applications of distributed parameter control theory of a survey; and dual variational inequalities for external eigenvalue problems. The book also ponders on stochastic differential equations in Hilbert space and their application to delay systems and linear quadratic optimal control problem over an infinite time horizon for a class of distributed parameter systems. The manuscript investigates the semigroup approach to boundary value control and stability of nonlinear distributed parameter systems. Topics include boundary control action implemented through a dynamical system; classical boundary value controls; stability of nonlinear systems; and feedback control on the boundary. The text also focuses on the functional analysis interpretation of Lyapunov stability; method of multipliers for a class distributed parameter systems; and digital transfer matrix approach to distributed system simulation. The selection is a dependable source of data for readers interested in the control of distributed parameter systems.