General Pontryagin Type Stochastic Maximum Principle And Backward Stochastic Evolution Equations In Infinite Dimensions

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General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

Author : Qi Lü
Publisher : Springer
ISBN 13 : 3319066323
Total Pages : 148 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions by : Qi Lü

Download or read book General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions written by Qi Lü and published by Springer. This book was released on 2014-06-02 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagin type maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.

General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

Author : Qi Lu
Publisher :
ISBN 13 : 9783319066332
Total Pages : 158 pages
Book Rating : 4.0/5 (663 download)

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Book Synopsis General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions by : Qi Lu

Download or read book General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions written by Qi Lu and published by . This book was released on 2014-06-30 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Control Theory for Stochastic Partial Differential Equations

Author : Qi Lü
Publisher : Springer Nature
ISBN 13 : 3030823318
Total Pages : 592 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Mathematical Control Theory for Stochastic Partial Differential Equations by : Qi Lü

Download or read book Mathematical Control Theory for Stochastic Partial Differential Equations written by Qi Lü and published by Springer Nature. This book was released on 2021-10-19 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Positivity and Noncommutative Analysis

Author : Gerard Buskes
Publisher : Springer
ISBN 13 : 3030108503
Total Pages : 604 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Positivity and Noncommutative Analysis by : Gerard Buskes

Download or read book Positivity and Noncommutative Analysis written by Gerard Buskes and published by Springer. This book was released on 2019-08-09 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Glück, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernández, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lü, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Román, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.

Control And Inverse Problems For Partial Differential Equations

Author : Bao Gang
Publisher : World Scientific
ISBN 13 : 9813276169
Total Pages : 264 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Control And Inverse Problems For Partial Differential Equations by : Bao Gang

Download or read book Control And Inverse Problems For Partial Differential Equations written by Bao Gang and published by World Scientific. This book was released on 2019-04-08 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of lecture notes for the LIASFMA Hangzhou Autumn School on 'Control and Inverse Problems for Partial Differential Equations' which was held during October 17-22, 2016 at Zhejiang University, Hangzhou, China. This autumn school is one of the activities organized by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA). Established jointly by eight institutions in China and France in 2014, LIASFMA aims at providing a platform for many leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in broad areas of applied mathematics.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in control and inverse problems. And the readers are exposed not only to the basic theories and methods but also to the forefront of research directions in both fields.

Numerical Control: Part A

Author :
Publisher : Elsevier
ISBN 13 : 0323853390
Total Pages : 596 pages
Book Rating : 4.3/5 (238 download)

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Book Synopsis Numerical Control: Part A by :

Download or read book Numerical Control: Part A written by and published by Elsevier. This book was released on 2022-02-15 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control

Stochastic Optimal Control in Infinite Dimension

Author : Giorgio Fabbri
Publisher : Springer
ISBN 13 : 3319530674
Total Pages : 916 pages
Book Rating : 4.3/5 (195 download)

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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.

Mathematical Control Theory for Stochastic Partial Differential Equations

Author : Qi Lü
Publisher : Springer
ISBN 13 : 9783030823337
Total Pages : 0 pages
Book Rating : 4.8/5 (233 download)

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Book Synopsis Mathematical Control Theory for Stochastic Partial Differential Equations by : Qi Lü

Download or read book Mathematical Control Theory for Stochastic Partial Differential Equations written by Qi Lü and published by Springer. This book was released on 2022-09-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optimal Feedback for Stochastic Linear Quadratic Control and Backward Stochastic Riccati Equations in Infinite Dimensions

Author : Qi Lü
Publisher : American Mathematical Society
ISBN 13 : 1470468751
Total Pages : 120 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Optimal Feedback for Stochastic Linear Quadratic Control and Backward Stochastic Riccati Equations in Infinite Dimensions by : Qi Lü

Download or read book Optimal Feedback for Stochastic Linear Quadratic Control and Backward Stochastic Riccati Equations in Infinite Dimensions written by Qi Lü and published by American Mathematical Society. This book was released on 2024-03-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Backward Stochastic Differential Equations

Author : N El Karoui
Publisher : CRC Press
ISBN 13 : 9780582307339
Total Pages : 236 pages
Book Rating : 4.3/5 (73 download)

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Book Synopsis Backward Stochastic Differential Equations by : N El Karoui

Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Stochastic Controls

Author : Jiongmin Yong
Publisher : Springer Science & Business Media
ISBN 13 : 1461214661
Total Pages : 459 pages
Book Rating : 4.4/5 (612 download)

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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.

Encyclopedia of Systems and Control

Author : John Baillieul
Publisher : Springer
ISBN 13 : 9781447150572
Total Pages : 1554 pages
Book Rating : 4.1/5 (55 download)

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Book Synopsis Encyclopedia of Systems and Control by : John Baillieul

Download or read book Encyclopedia of Systems and Control written by John Baillieul and published by Springer. This book was released on 2015-07-29 with total page 1554 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Systems and Control collects a broad range of short expository articles that describe the current state of the art in the central topics of control and systems engineering as well as in many of the related fields in which control is an enabling technology. The editors have assembled the most comprehensive reference possible, and this has been greatly facilitated by the publisher’s commitment continuously to publish updates to the articles as they become available in the future. Although control engineering is now a mature discipline, it remains an area in which there is a great deal of research activity, and as new developments in both theory and applications become available, they will be included in the online version of the encyclopedia. A carefully chosen team of leading authorities in the field has written the well over 250 articles that comprise the work. The topics range from basic principles of feedback in servomechanisms to advanced topics such as the control of Boolean networks and evolutionary game theory. Because the content has been selected to reflect both foundational importance as well as subjects that are of current interest to the research and practitioner communities, a broad readership that includes students, application engineers, and research scientists will find material that is of interest.

The Robust Maximum Principle

Author : Vladimir G. Boltyanski
Publisher : Springer Science & Business Media
ISBN 13 : 0817681523
Total Pages : 440 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Robust Maximum Principle by : Vladimir G. Boltyanski

Download or read book The Robust Maximum Principle written by Vladimir G. Boltyanski and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering some of the key areas of optimal control theory (OCT), a rapidly expanding field, the authors use new methods to set out a version of OCT’s more refined ‘maximum principle.’ The results obtained have applications in production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games. This book explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control.

Calculus of Variations and Optimal Control Theory

Author : Daniel Liberzon
Publisher : Princeton University Press
ISBN 13 : 0691151873
Total Pages : 255 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon

Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

Stochastic Evolution Equations

Author : Wilfried Grecksch
Publisher : De Gruyter Akademie Forschung
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Stochastic Evolution Equations by : Wilfried Grecksch

Download or read book Stochastic Evolution Equations written by Wilfried Grecksch and published by De Gruyter Akademie Forschung. This book was released on 1995 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.

Dynamic Optimization, Second Edition

Author : Morton I. Kamien
Publisher : Courier Corporation
ISBN 13 : 0486310280
Total Pages : 402 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Dynamic Optimization, Second Edition by : Morton I. Kamien

Download or read book Dynamic Optimization, Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

Optimal Control Theory with Applications in Economics

Author : Thomas A. Weber
Publisher : MIT Press
ISBN 13 : 0262015730
Total Pages : 387 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Optimal Control Theory with Applications in Economics by : Thomas A. Weber

Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.