Stochastic Optimal Control In Infinite Dimension
DOWNLOAD
Download Stochastic Optimal Control In Infinite Dimension PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Stochastic Optimal Control In Infinite Dimension book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Stochastic Optimal Control In Infinite Dimension
DOWNLOAD
Author : Giorgio Fabbri
language : en
Publisher: Springer
Release Date : 2017-06-22
Stochastic Optimal Control In Infinite Dimension written by Giorgio Fabbri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-22 with Mathematics categories.
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.
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics
DOWNLOAD
Author : Wilfried Grecksch
language : en
Publisher: World Scientific
Release Date : 2020-04-22
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Science categories.
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Second Order Pde S In Finite And Infinite Dimension
DOWNLOAD
Author : Sandra Cerrai
language : en
Publisher: Springer
Release Date : 2003-07-01
Second Order Pde S In Finite And Infinite Dimension written by Sandra Cerrai 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.
The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. We focus our attention on the regularity properties of the solutions and hence on the smoothing effect of the corresponding transition semigroups in the space of bounded and uniformly continuous functions. As an application of these results, we study the associated Kolmogorov equations, the large-time behaviour of the solutions and some stochastic optimal control problems together with the corresponding Hamilton- Jacobi-Bellman equations. In the literature there exists a large number of works (mostly in finite dimen sion) dealing with these arguments in the case of bounded Lipschitz-continuous coefficients and some of them concern the case of coefficients having linear growth. Few papers concern the case of non-Lipschitz coefficients, but they are mainly re lated to the study of the existence and the uniqueness of solutions for the stochastic system. Actually, the study of any further properties of those systems, such as their regularizing properties or their ergodicity, seems not to be developed widely enough. With these notes we try to cover this gap.
Infinite Dimensional Optimization And Control Theory
DOWNLOAD
Author : Hector O. Fattorini
language : en
Publisher: Cambridge University Press
Release Date : 1999-03-28
Infinite Dimensional Optimization And Control Theory written by Hector O. Fattorini and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-28 with Computers categories.
Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.
Time Delayed Linear Quadratic Optimal Control Problems
DOWNLOAD
Author : Weijun Meng
language : en
Publisher: Springer Nature
Release Date : 2025-02-22
Time Delayed Linear Quadratic Optimal Control Problems written by Weijun Meng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-22 with Science categories.
This book characterizes the open-loop and closed-loop solvability for time-delayed linear quadratic optimal control problems. Different from the existing literature, in the current book, we present a theory of deterministic LQ problems with delays which has several new features: Our system is time-varying, with both the state equation and cost functional being allowed to include discrete and distributed delays, both in the state and the control. We take different approaches to discuss the unboundedness of the control operator. The open-loop solvability of the lifted problem is characterized by the solvability of a system of forward-backward integral evolution equations and the convexity condition of the cost functional. Surprisingly, the adjoint equations involve some coupled partial differential equations, which is significantly different from that in the literature, where, the adjoint equations are all some anticipated backward ordinary differential equations. The closed-loop solvability is characterized by the solvability of three equivalent integral operator-valued Riccati equations and two equivalent backward integral evolution equations which are much easier to handle than the differential operator-valued Riccati equations used in the literature to study similar problems. The closed-loop representation of open-loop optimal control is presented through three equivalent integral operator-valued Riccati equations.
Optimal Control Of Dynamic Systems Driven By Vector Measures
DOWNLOAD
Author : N. U. Ahmed
language : en
Publisher: Springer Nature
Release Date : 2021-09-13
Optimal Control Of Dynamic Systems Driven By Vector Measures written by N. U. Ahmed and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-13 with Mathematics categories.
This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
Stochastic Partial Differential Equations And Applications Vii
DOWNLOAD
Author : Giuseppe Da Prato
language : en
Publisher: CRC Press
Release Date : 2005-10-12
Stochastic Partial Differential Equations And Applications Vii written by Giuseppe Da Prato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-12 with Mathematics categories.
Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this boo
Neural Approximations For Optimal Control And Decision
DOWNLOAD
Author : Riccardo Zoppoli
language : en
Publisher: Springer Nature
Release Date : 2019-12-17
Neural Approximations For Optimal Control And Decision written by Riccardo Zoppoli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-17 with Technology & Engineering categories.
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.
Optimal Control Of Infinite Dimensional Stochastic Systems
DOWNLOAD
Author : Qingxin Zhu
language : en
Publisher:
Release Date : 1993
Optimal Control Of Infinite Dimensional Stochastic Systems written by Qingxin Zhu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Control theory categories.
In this thesis we study a Hamilton-Jacobi-Bellman equation arising from the stochastic optimal control problem. More precisely, we study the following second order parabolic partial differential equation$$(P)\left\{\eqalign{&\phi\sb{t}(t,x)={1\over 2}Tr(S\phi\sb{xx}(t,x))+(Bx + \int(x),\phi\sb{x}(t,x))\cr&\qquad\qquad + F(t,x,\phi(t,x),\phi\sb{x}(t,x))\cr&\phi(0,x)=\phi\sb0(x)\right. \cr}$$Where $\phi\sb0,F$ are given functions, B is the infinitesimal generator of a strongly continuous semigroup, and S is a positive, self-adjoint nuclear operator in a Banach space X (Chapter 3) or an identity operator in ${\cal L}(X\sp\*,X)$ (Chapter 4).
Measure Valued Solutions For Nonlinear Evolution Equations On Banach Spaces And Their Optimal Control
DOWNLOAD
Author : N. U. Ahmed
language : en
Publisher: Springer Nature
Release Date : 2023-09-12
Measure Valued Solutions For Nonlinear Evolution Equations On Banach Spaces And Their Optimal Control written by N. U. Ahmed and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-12 with Mathematics categories.
This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.