Stochastic Theory And Control
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Stochastic Theory And Control
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Author : Bozenna Pasik-Duncan
language : en
Publisher: Springer
Release Date : 2003-07-01
Stochastic Theory And Control written by Bozenna Pasik-Duncan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
This volume contains almost all of the papers that were presented at the Workshop on Stochastic Theory and Control that was held at the Univ- sity of Kansas, 18–20 October 2001. This three-day event gathered a group of leading scholars in the ?eld of stochastic theory and control to discuss leading-edge topics of stochastic control, which include risk sensitive control, adaptive control, mathematics of ?nance, estimation, identi?cation, optimal control, nonlinear ?ltering, stochastic di?erential equations, stochastic p- tial di?erential equations, and stochastic theory and its applications. The workshop provided an opportunity for many stochastic control researchers to network and discuss cutting-edge technologies and applications, teaching and future directions of stochastic control. Furthermore, the workshop focused on promoting control theory, in particular stochastic control, and it promoted collaborative initiatives in stochastic theory and control and stochastic c- trol education. The lecture on “Adaptation of Real-Time Seizure Detection Algorithm” was videotaped by the PBS. Participants of the workshop have been involved in contributing to the documentary being ?lmed by PBS which highlights the extraordinary work on “Math, Medicine and the Mind: Discovering Tre- ments for Epilepsy” that examines the e?orts of the multidisciplinary team on which several of the participants of the workshop have been working for many years to solve one of the world’s most dramatic neurological conditions. Invited high school teachers of Math and Science were among the part- ipants of this professional meeting.
Stochastic Control Theory
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Author : Makiko Nisio
language : en
Publisher: Springer
Release Date : 2014-11-27
Stochastic Control Theory written by Makiko Nisio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Mathematics categories.
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.
Stochastic Control In Insurance
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Author : Hanspeter Schmidli
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-20
Stochastic Control In Insurance written by Hanspeter Schmidli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-20 with Business & Economics categories.
Yet again, here is a Springer volume that offers readers something completely new. Until now, solved examples of the application of stochastic control to actuarial problems could only be found in journals. Not any more: this is the first book to systematically present these methods in one volume. The author starts with a short introduction to stochastic control techniques, then applies the principles to several problems. These examples show how verification theorems and existence theorems may be proved, and that the non-diffusion case is simpler than the diffusion case. Schmidli’s brilliant text also includes a number of appendices, a vital resource for those in both academic and professional settings.
Introduction To Stochastic Control Theory
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Author : Karl J. Åström
language : en
Publisher: Courier Corporation
Release Date : 2012-05-11
Introduction To Stochastic Control Theory written by Karl J. Åström and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-11 with Technology & Engineering categories.
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.
Stochastic Processes Optimization And Control Theory Applications In Financial Engineering Queueing Networks And Manufacturing Systems
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Author : Houmin Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-10
Stochastic Processes Optimization And Control Theory Applications In Financial Engineering Queueing Networks And Manufacturing Systems written by Houmin Yan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-10 with Technology & Engineering categories.
This edited volume contains 16 research articles. It presents recent and pressing issues in stochastic processes, control theory, differential games, optimization, and their applications in finance, manufacturing, queueing networks, and climate control. One of the salient features is that the book is highly multi-disciplinary. The book is dedicated to Professor Suresh Sethi on the occasion of his 60th birthday, in view of his distinguished career.
Control Theory Stochastic Analysis And Applications Proceedings Of Symposium On System Sciences And Control Theory
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Author : S P Chen
language : en
Publisher: World Scientific
Release Date : 1992-03-27
Control Theory Stochastic Analysis And Applications Proceedings Of Symposium On System Sciences And Control Theory written by S P Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-27 with categories.
The symposium discusses and explores the current and future development of some aspects of the theory of nonlinear control systems, adaptive control and filtering, robust control and H∞ optimization, stochastic systems and white noise analysis, etc.
Control And System Theory Of Discrete Time Stochastic Systems
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Author : Jan H. van Schuppen
language : en
Publisher: Springer Nature
Release Date : 2021-08-02
Control And System Theory Of Discrete Time Stochastic Systems written by Jan H. van Schuppen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Technology & Engineering categories.
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.
Linear Stochastic Control Systems
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Author : Goong Chen
language : en
Publisher: CRC Press
Release Date : 1995-07-12
Linear Stochastic Control Systems written by Goong Chen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-12 with Business & Economics categories.
Linear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered. Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.
Mathematical Control Theory For Stochastic Partial Differential Equations
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Author : Qi Lü
language : en
Publisher: Springer Nature
Release Date : 2021-10-19
Mathematical Control Theory For Stochastic Partial Differential Equations written by Qi Lü and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-19 with Science categories.
This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.
Stochastic Control In Discrete And Continuous Time
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Author : Atle Seierstad
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-03
Stochastic Control In Discrete And Continuous Time written by Atle Seierstad and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-03 with Mathematics categories.
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.