Finite Approximations In Discrete Time Stochastic Control

Author : Naci Saldi,Tamás Linder,Serdar Yüksel
Publisher : Birkhäuser
Page : 198 pages
File Size : 53,7 Mb
Release : 2018-05-11
Category : Mathematics
ISBN : 9783319790336

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Finite Approximations in Discrete-Time Stochastic Control by Naci Saldi,Tamás Linder,Serdar Yüksel Pdf

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.

Author : Atle Seierstad
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 43,8 Mb
Release : 2010-07-03
Category : Mathematics
ISBN : 9780387766171

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Stochastic Control in Discrete and Continuous Time by Atle Seierstad Pdf

This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems (Chapter 3), and control of Ito diffusions (Chapter 4). The chapters include treatments of optimal stopping problems. An Appendix - calls material from elementary probability theory and gives heuristic explanations of certain more advanced tools in probability theory. The book will hopefully be of interest to students in several ?elds: economics, engineering, operations research, ?nance, business, mathematics. In economics and business administration, graduate students should readily be able to read it, and the mathematical level can be suitable for advanced undergraduates in mathem- ics and science. The prerequisites for reading the book are only a calculus course and a course in elementary probability. (Certain technical comments may demand a slightly better background. ) As this book perhaps (and hopefully) will be read by readers with widely diff- ing backgrounds, some general advice may be useful: Don’t be put off if paragraphs, comments, or remarks contain material of a seemingly more technical nature that you don’t understand. Just skip such material and continue reading, it will surely not be needed in order to understand the main ideas and results. The presentation avoids the use of measure theory.

Author : Harold Kushner,Paul G. Dupuis
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468404418

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Numerical Methods for Stochastic Control Problems in Continuous Time by Harold Kushner,Paul G. Dupuis Pdf

This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new prob lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for mulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. Both the "drift" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.

Author : Riccardo Zoppoli,Marcello Sanguineti,Giorgio Gnecco,Thomas Parisini
Publisher : Springer Nature
Page : 532 pages
File Size : 40,9 Mb
Release : 2019-12-17
Category : Technology & Engineering
ISBN : 9783030296933

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Neural Approximations for Optimal Control and Decision by Riccardo Zoppoli,Marcello Sanguineti,Giorgio Gnecco,Thomas Parisini Pdf

Neural Approximations for Optimal Control and Decision provides a comprehensive methodology for the approximate solution of functional optimization problems using neural networks and other nonlinear approximators where the use of traditional optimal control tools is prohibited by complicating factors like non-Gaussian noise, strong nonlinearities, large dimension of state and control vectors, etc. Features of the text include: • a general functional optimization framework; • thorough illustration of recent theoretical insights into the approximate solutions of complex functional optimization problems; • comparison of classical and neural-network based methods of approximate solution; • bounds to the errors of approximate solutions; • solution algorithms for optimal control and decision in deterministic or stochastic environments with perfect or imperfect state measurements over a finite or infinite time horizon and with one decision maker or several; • applications of current interest: routing in communications networks, traffic control, water resource management, etc.; and • numerous, numerically detailed examples. The authors’ diverse backgrounds in systems and control theory, approximation theory, machine learning, and operations research lend the book a range of expertise and subject matter appealing to academics and graduate students in any of those disciplines together with computer science and other areas of engineering.

Author : Jan H. van Schuppen
Publisher : Springer Nature
Page : 940 pages
File Size : 43,6 Mb
Release : 2021-08-02
Category : Technology & Engineering
ISBN : 9783030669522

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Control and System Theory of Discrete-Time Stochastic Systems by Jan H. van Schuppen Pdf

This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time stochastic systems so that they can then apply its principles to their own stochastic control systems and to the solution of control, filtering, and realization problems for such systems. Applications of the theory in the book include the control of ships, shock absorbers, traffic and communications networks, and power systems with fluctuating power flows. The focus of the book is a stochastic control system defined for a spectrum of probability distributions including Bernoulli, finite, Poisson, beta, gamma, and Gaussian distributions. The concepts of observability and controllability of a stochastic control system are defined and characterized. Each output process considered is, with respect to conditions, represented by a stochastic system called a stochastic realization. The existence of a control law is related to stochastic controllability while the existence of a filter system is related to stochastic observability. Stochastic control with partial observations is based on the existence of a stochastic realization of the filtration of the observed process.​

Author : Harold J. Kushner,Paul Dupuis
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 45,7 Mb
Release : 2001
Category : Language Arts & Disciplines
ISBN : 0387951393

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Numerical Methods for Stochastic Control Problems in Continuous Time by Harold J. Kushner,Paul Dupuis Pdf

The required background is surveyed, and there is an extensive development of methods of approximation and computational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience."--BOOK JACKET.

Author : Alexey Piunovskiy,Yi Zhang
Publisher : Springer Nature
Page : 356 pages
File Size : 52,8 Mb
Release : 2021-06-04
Category : Technology & Engineering
ISBN : 9783030769284

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Modern Trends in Controlled Stochastic Processes: by Alexey Piunovskiy,Yi Zhang Pdf

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. ​

Author : Paolo Brandimarte
Publisher : Springer Nature
Page : 216 pages
File Size : 42,8 Mb
Release : 2021-01-11
Category : Business & Economics
ISBN : 9783030618674

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From Shortest Paths to Reinforcement Learning by Paolo Brandimarte Pdf

Dynamic programming (DP) has a relevant history as a powerful and flexible optimization principle, but has a bad reputation as a computationally impractical tool. This book fills a gap between the statement of DP principles and their actual software implementation. Using MATLAB throughout, this tutorial gently gets the reader acquainted with DP and its potential applications, offering the possibility of actual experimentation and hands-on experience. The book assumes basic familiarity with probability and optimization, and is suitable to both practitioners and graduate students in engineering, applied mathematics, management, finance and economics.

Author : Serdar Yüksel
Publisher : Springer Nature
Page : 935 pages
File Size : 50,8 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031540714

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Stochastic Teams, Games, and Control under Information Constraints by Serdar Yüksel Pdf

Author : Harold Kushner
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 43,8 Mb
Release : 2008-12-19
Category : Science
ISBN : 9780817646219

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Numerical Methods for Controlled Stochastic Delay Systems by Harold Kushner Pdf

The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. The book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is either in the use of the algorithms or in the mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.

Author : Farhad Farokhi
Publisher : Springer Nature
Page : 290 pages
File Size : 41,7 Mb
Release : 2019-11-21
Category : Technology & Engineering
ISBN : 9789811504938

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Privacy in Dynamical Systems by Farhad Farokhi Pdf

This book addresses privacy in dynamical systems, with applications to smart metering, traffic estimation, and building management. In the first part, the book explores statistical methods for privacy preservation from the areas of differential privacy and information-theoretic privacy (e.g., using privacy metrics motivated by mutual information, relative entropy, and Fisher information) with provable guarantees. In the second part, it investigates the use of homomorphic encryption for the implementation of control laws over encrypted numbers to support the development of fully secure remote estimation and control. Chiefly intended for graduate students and researchers, the book provides an essential overview of the latest developments in privacy-aware design for dynamical systems.

Author : Charles S. Tapiero
Publisher : Routledge
Page : 410 pages
File Size : 49,7 Mb
Release : 2018-04-17
Category : Business & Economics
ISBN : 9781351243209

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Managerial Planning by Charles S. Tapiero Pdf

Originally published in 1977. Management is a dynamic process reflected in three essential functions: management of time, change and people. The book provides a bridging gap between quantitative theories imbedded in the systems approach and managerial decision-making over time and under risk. The conventional wisdom that management is a dynamic process is rendered operational. This title will be of interest to students of business studies and management.

Author : George Yin,Qing Zhang
Publisher : Springer
Page : 599 pages
File Size : 44,7 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9783030254988

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Modeling, Stochastic Control, Optimization, and Applications by George Yin,Qing Zhang Pdf

This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Author : Karl J. Åström
Publisher : Courier Corporation
Page : 322 pages
File Size : 41,7 Mb
Release : 2012-05-11
Category : Technology & Engineering
ISBN : 9780486138275

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Introduction to Stochastic Control Theory by Karl J. Åström Pdf

This text for upper-level undergraduates and graduate students explores stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear systems with quadratic criteria, it covers discrete time as well as continuous time systems. The first three chapters provide motivation and background material on stochastic processes, followed by an analysis of dynamical systems with inputs of stochastic processes. A simple version of the problem of optimal control of stochastic systems is discussed, along with an example of an industrial application of this theory. Subsequent discussions cover filtering and prediction theory as well as the general stochastic control problem for linear systems with quadratic criteria. Each chapter begins with the discrete time version of a problem and progresses to a more challenging continuous time version of the same problem. Prerequisites include courses in analysis and probability theory in addition to a course in dynamical systems that covers frequency response and the state-space approach for continuous time and discrete time systems.

Author : Mou-Hsiung Chang
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 49,5 Mb
Release : 2008-01-03
Category : Mathematics
ISBN : 9780387758169

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Stochastic Control of Hereditary Systems and Applications by Mou-Hsiung Chang Pdf

This monograph develops the Hamilton-Jacobi-Bellman theory via dynamic programming principle for a class of optimal control problems for stochastic hereditary differential equations (SHDEs) driven by a standard Brownian motion and with a bounded or an infinite but fading memory. These equations represent a class of stochastic infinite-dimensional systems that become increasingly important and have wide range of applications in physics, chemistry, biology, engineering and economics/finance. This monograph can be used as a reference for those who have special interest in optimal control theory and applications of stochastic hereditary systems.