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Introduction To Stochastic Control Theory
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Book Synopsis Stochastic Control Theory by : Makiko Nisio
Download or read book Stochastic Control Theory written by Makiko Nisio and published by Springer. This book was released on 2014-11-27 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.
Book Synopsis Introduction to Stochastic Control Theory by : Karl J. Åström
Download or read book Introduction to Stochastic Control Theory written by Karl J. Åström and published by Courier Corporation. This book was released on 2012-05-11 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Control in Discrete and Continuous Time by : Atle Seierstad
Download or read book Stochastic Control in Discrete and Continuous Time written by Atle Seierstad and published by Springer Science & Business Media. This book was released on 2010-07-03 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Estimation by : Frank L. Lewis
Download or read book Optimal Estimation written by Frank L. Lewis and published by Wiley-Interscience. This book was released on 1986-04-15 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the use of optimal control and estimation in the design of robots, controlled mechanisms, and navigation and guidance systems. Covers control theory specifically for students with minimal background in probability theory. Presents optimal estimation theory as a tutorial with a direct, well-organized approach and a parallel treatment of discrete and continuous time systems. Gives practical examples and computer simulations. Provides enough mathematical rigor to put results on a firm foundation without an overwhelming amount of proofs and theorems.
Book Synopsis Optimal and Robust Estimation by : Frank L. Lewis
Download or read book Optimal and Robust Estimation written by Frank L. Lewis and published by CRC Press. This book was released on 2017-12-19 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than a decade ago, world-renowned control systems authority Frank L. Lewis introduced what would become a standard textbook on estimation, under the title Optimal Estimation, used in top universities throughout the world. The time has come for a new edition of this classic text, and Lewis enlisted the aid of two accomplished experts to bring the book completely up to date with the estimation methods driving today's high-performance systems. A Classic Revisited Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition reflects new developments in estimation theory and design techniques. As the title suggests, the major feature of this edition is the inclusion of robust methods. Three new chapters cover the robust Kalman filter, H-infinity filtering, and H-infinity filtering of discrete-time systems. Modern Tools for Tomorrow's Engineers This text overflows with examples that highlight practical applications of the theory and concepts. Design algorithms appear conveniently in tables, allowing students quick reference, easy implementation into software, and intuitive comparisons for selecting the best algorithm for a given application. In addition, downloadable MATLAB® code allows students to gain hands-on experience with industry-standard software tools for a wide variety of applications. This cutting-edge and highly interactive text makes teaching, and learning, estimation methods easier and more modern than ever.
Book Synopsis Stochastic Controls by : Jiongmin Yong
Download or read book Stochastic Controls written by Jiongmin Yong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation.
Book Synopsis Optimal Control and Estimation by : Robert F. Stengel
Download or read book Optimal Control and Estimation written by Robert F. Stengel and published by Courier Corporation. This book was released on 2012-10-16 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.
Book Synopsis Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions by : Jingrui Sun
Download or read book Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions written by Jingrui Sun and published by Springer Nature. This book was released on 2020-06-29 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Optimal Control in Infinite Dimension by : Giorgio Fabbri
Download or read book Stochastic Optimal Control in Infinite Dimension written by Giorgio Fabbri and published by Springer. This book was released on 2017-06-22 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Deterministic and Stochastic Optimal Control by : Wendell H. Fleming
Download or read book Deterministic and Stochastic Optimal Control written by Wendell H. Fleming and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of Deterministic and Stochastic Control by : Jon H. Davis
Download or read book Foundations of Deterministic and Stochastic Control written by Jon H. Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume is a textbook on linear control systems with an emphasis on stochastic optimal control with solution methods using spectral factorization in line with the original approach of N. Wiener. Continuous-time and discrete-time versions are presented in parallel.... Two appendices introduce functional analytic concepts and probability theory, and there are 77 references and an index. The chapters (except for the last two) end with problems.... [T]he book presents in a clear way important concepts of control theory and can be used for teaching." —Zentralblatt Math "This is a textbook intended for use in courses on linear control and filtering and estimation on (advanced) levels. Its major purpose is an introduction to both deterministic and stochastic control and estimation. Topics are treated in both continuous time and discrete time versions.... Each chapter involves problems and exercises, and the book is supplemented by appendices, where fundamentals on Hilbert and Banach spaces, operator theory, and measure theoretic probability may be found. The book will be very useful for students, but also for a variety of specialists interested in deterministic and stochastic control and filtering." —Applications of Mathematics "The strength of the book under review lies in the choice of specialized topics it contains, which may not be found in this form elsewhere. Also, the first half would make a good standard course in linear control." —Journal of the Indian Institute of Science
Book Synopsis Introduction to Stochastic Search and Optimization by : James C. Spall
Download or read book Introduction to Stochastic Search and Optimization written by James C. Spall and published by John Wiley & Sons. This book was released on 2005-03-11 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Unique in its survey of the range of topics. * Contains a strong, interdisciplinary format that will appeal to both students and researchers. * Features exercises and web links to software and data sets.
Book Synopsis Mathematical Control Theory by : Jerzy Zabczyk
Download or read book Mathematical Control Theory written by Jerzy Zabczyk and published by Springer Science & Business Media. This book was released on 2008 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a mathematically precise manner, this book presents a unified introduction to deterministic control theory. It includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems.
Book Synopsis Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by : Rene Carmona
Download or read book Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications written by Rene Carmona and published by SIAM. This book was released on 2016-02-18 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.
Book Synopsis Continuous-time Stochastic Control and Optimization with Financial Applications by : Huyên Pham
Download or read book Continuous-time Stochastic Control and Optimization with Financial Applications written by Huyên Pham and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.
Book Synopsis Numerical Methods for Stochastic Control Problems in Continuous Time by : Harold Kushner
Download or read book Numerical Methods for Stochastic Control Problems in Continuous Time written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.
Book Synopsis Primer on Optimal Control Theory by : Jason L. Speyer
Download or read book Primer on Optimal Control Theory written by Jason L. Speyer and published by SIAM. This book was released on 2010-05-13 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, which will enable engineers and scientists to put the theory into practice.
