Infinite Dimensional Optimization And Control Theory
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Infinite Dimensional Optimization And Control Theory
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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.
Infinite Dimensional Optimization And Control Theory
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Author : Hector O. Fattorini
language : en
Publisher:
Release Date : 2014-05-14
Infinite Dimensional Optimization And Control Theory written by Hector O. Fattorini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with COMPUTERS categories.
Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.
Optimal Control Theory For Infinite Dimensional Systems
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Author : Xungjing Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Optimal Control Theory For Infinite Dimensional Systems written by Xungjing Li 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 2012-12-06 with Mathematics categories.
Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.
Stochastic Optimal Control In Infinite Dimension
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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.
General Pontryagin Type Stochastic Maximum Principle And Backward Stochastic Evolution Equations In Infinite Dimensions
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Author : Qi Lü
language : en
Publisher: Springer
Release Date : 2014-06-02
General Pontryagin Type Stochastic Maximum Principle And Backward Stochastic Evolution Equations In Infinite Dimensions written by Qi Lü and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-02 with Science categories.
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.
Representation And Control Of Infinite Dimensional Systems
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Author : Alain Bensoussan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-05
Representation And Control Of Infinite Dimensional Systems written by Alain Bensoussan 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 2007-04-05 with Technology & Engineering categories.
This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
Optimization And Control Techniques And Applications
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Author : Honglei Xu
language : en
Publisher: Springer
Release Date : 2014-06-26
Optimization And Control Techniques And Applications written by Honglei Xu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-26 with Mathematics categories.
This book presents advances in state-of-the-art solution methods and their applications to real life practical problems in optimization, control and operations research. Contributions from world-class experts in the field are collated here in two parts, dealing first with optimization and control theory and then with techniques and applications. Topics covered in the first part include control theory on infinite dimensional Banach spaces, history-dependent inclusion and linear programming complexity theory. Chapters also explore the use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems and look at multi-objective semi-infinite optimization problems and production planning problems. In the second part, the authors address techniques and applications of optimization and control in a variety of disciplines, such as chaos synchronization, facial expression recognition and dynamic input-output economic models. Other applications considered here include image retrieval, natural earth satellites orbital transfers, snap-back repellers and modern logistic systems. Readers will learn of advances in optimization, control and operations research, as well as potential new avenues of research and development. The book will appeal to scientific researchers, mathematicians and all specialists interested in the latest advances in optimization and control.
Trends In Control Theory And Partial Differential Equations
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Author : Fatiha Alabau-Boussouira
language : en
Publisher: Springer
Release Date : 2019-07-04
Trends In Control Theory And Partial Differential Equations written by Fatiha Alabau-Boussouira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-04 with Mathematics categories.
This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.
Representation And Control Of Infinite Dimensional Systems
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Author : Alain Bensoussan
language : en
Publisher: Birkhäuser
Release Date : 2008-11-01
Representation And Control Of Infinite Dimensional Systems written by Alain Bensoussan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Technology & Engineering categories.
This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
Infinite Dimensional Optimization And Convexity
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Author : Ivar Ekeland
language : en
Publisher: University of Chicago Press
Release Date : 1983-09-15
Infinite Dimensional Optimization And Convexity written by Ivar Ekeland and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-09-15 with Business & Economics categories.
The caratheodory approach; Infinite-dimensional optimization; Duality theory.