Stochastic Optimal Control The Discrete Time Case

Author : Dimitri Bertsekas,Steven E. Shreve
Publisher : Athena Scientific
Page : 336 pages
File Size : 40,7 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 9781886529038

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Stochastic Optimal Control: The Discrete-Time Case by Dimitri Bertsekas,Steven E. Shreve Pdf

This research monograph, first published in 1978 by Academic Press, remains the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including the treatment of the intricate measure-theoretic issues. It is an excellent supplement to the first author's Dynamic Programming and Optimal Control (Athena Scientific, 2018). Review of the 1978 printing:"Bertsekas and Shreve have written a fine book. The exposition is extremely clear and a helpful introductory chapter provides orientation and a guide to the rather intimidating mass of literature on the subject. Apart from anything else, the book serves as an excellent introduction to the arcane world of analytic sets and other lesser known byways of measure theory." Mark H. A. Davis, Imperial College, in IEEE Trans. on Automatic Control Among its special features, the book: 1) Resolves definitively the mathematical issues of discrete-time stochastic optimal control problems, including Borel models, and semi-continuous models 2) Establishes the most general possible theory of finite and infinite horizon stochastic dynamic programming models, through the use of analytic sets and universally measurable policies 3) Develops general frameworks for dynamic programming based on abstract contraction and monotone mappings 4) Provides extensive background on analytic sets, Borel spaces and their probability measures 5) Contains much in depth research not found in any other textbook

Author : Atle Seierstad
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 49,5 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 : C. Striebel
Publisher : Springer
Page : 215 pages
File Size : 44,6 Mb
Release : 2013-12-21
Category : Business & Economics
ISBN : 9783642454707

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Optimal Control of Discrete Time Stochastic Systems by C. Striebel Pdf

Author : Dimitri P. Bertsekas
Publisher : Unknown
Page : 543 pages
File Size : 54,6 Mb
Release : 2005
Category : Mathematics
ISBN : 1886529264

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Dynamic Programming and Optimal Control by Dimitri P. Bertsekas Pdf

"The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning. The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use. The second volume is oriented towards mathematical analysis and computation, treats infinite horizon problems extensively, and provides an up-to-date account of approximate large-scale dynamic programming and reinforcement learning. The text contains many illustrations, worked-out examples, and exercises."--Publisher's website.

Author : Joël Blot,Naïla Hayek
Publisher : Springer Science & Business Media
Page : 130 pages
File Size : 43,9 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.

Author : Jan H. van Schuppen
Publisher : Springer Nature
Page : 940 pages
File Size : 55,7 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 : Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Publisher : Springer
Page : 916 pages
File Size : 53,6 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9783319530673

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Stochastic Optimal Control in Infinite Dimension by Giorgio Fabbri,Fausto Gozzi,Andrzej Święch Pdf

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.

Author : Robert F. Stengel
Publisher : Courier Corporation
Page : 672 pages
File Size : 50,6 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9780486134819

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Optimal Control and Estimation by Robert F. Stengel Pdf

Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 129 pages
File Size : 46,7 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030209223

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Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions by Jingrui Sun,Jiongmin Yong Pdf

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Author : Onésimo Hernández-Lerma,Leonardo R. Laura-Guarachi,Saul Mendoza-Palacios,David González-Sánchez
Publisher : Springer Nature
Page : 279 pages
File Size : 44,7 Mb
Release : 2023-02-21
Category : Mathematics
ISBN : 9783031211393

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An Introduction to Optimal Control Theory by Onésimo Hernández-Lerma,Leonardo R. Laura-Guarachi,Saul Mendoza-Palacios,David González-Sánchez Pdf

This book introduces optimal control problems for large families of deterministic and stochastic systems with discrete or continuous time parameter. These families include most of the systems studied in many disciplines, including Economics, Engineering, Operations Research, and Management Science, among many others. The main objective is to give a concise, systematic, and reasonably self contained presentation of some key topics in optimal control theory. To this end, most of the analyses are based on the dynamic programming (DP) technique. This technique is applicable to almost all control problems that appear in theory and applications. They include, for instance, finite and infinite horizon control problems in which the underlying dynamic system follows either a deterministic or stochastic difference or differential equation. In the infinite horizon case, it also uses DP to study undiscounted problems, such as the ergodic or long-run average cost. After a general introduction to control problems, the book covers the topic dividing into four parts with different dynamical systems: control of discrete-time deterministic systems, discrete-time stochastic systems, ordinary differential equations, and finally a general continuous-time MCP with applications for stochastic differential equations. The first and second part should be accessible to undergraduate students with some knowledge of elementary calculus, linear algebra, and some concepts from probability theory (random variables, expectations, and so forth). Whereas the third and fourth part would be appropriate for advanced undergraduates or graduate students who have a working knowledge of mathematical analysis (derivatives, integrals, ...) and stochastic processes.

Author : Naci Saldi,Tamás Linder,Serdar Yüksel
Publisher : Birkhäuser
Page : 198 pages
File Size : 42,9 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 : Charlotte Striebel
Publisher : Springer
Page : 0 pages
File Size : 48,7 Mb
Release : 1975
Category : Commande, Théorie de la
ISBN : 0387071814

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Optimal Control of Discrete Time Stochastic Systems by Charlotte Striebel Pdf

Author : Onesimo Hernandez-Lerma,Jean B. Lasserre
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205616

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Further Topics on Discrete-Time Markov Control Processes by Onesimo Hernandez-Lerma,Jean B. Lasserre Pdf

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.

Author : Wendell H. Fleming,Raymond W. Rishel
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263807

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Deterministic and Stochastic Optimal Control by Wendell H. Fleming,Raymond W. Rishel Pdf

This book may be regarded as consisting of two parts. In Chapters I-IV we pre sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro gramming method, and depends on the intimate relationship between second order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.

Author : Peter S. Maybeck
Publisher : Academic Press
Page : 291 pages
File Size : 53,6 Mb
Release : 1982-08-25
Category : Mathematics
ISBN : 0080960030

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Stochastic Models, Estimation, and Control by Peter S. Maybeck Pdf

This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.