Control Theory Of Infinite Dimensional Systems
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Control Theory Of Infinite Dimensional Systems
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Author : Joachim Kerner
language : en
Publisher: Springer Nature
Release Date : 2020-06-25
Control Theory Of Infinite Dimensional Systems written by Joachim Kerner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-25 with Science categories.
This book presents novel results by participants of the conference “Control theory of infinite-dimensional systems” that took place in January 2018 at the FernUniversität in Hagen. Topics include well-posedness, controllability, optimal control problems as well as stability of linear and nonlinear systems, and are covered by world-leading experts in these areas. A distinguishing feature of the contributions in this volume is the particular combination of researchers from different fields in mathematics working in an interdisciplinary fashion on joint projects in mathematical system theory. More explicitly, the fields of partial differential equations, semigroup theory, mathematical physics, graph and network theory as well as numerical analysis are all well-represented.
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.
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.
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.
Stability Of Finite And Infinite Dimensional Systems
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Author : Michael I. Gil'
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-30
Stability Of Finite And Infinite Dimensional Systems written by Michael I. Gil' 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 1998-09-30 with Mathematics categories.
The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
Introduction To Infinite Dimensional Systems Theory
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Author : Ruth Curtain
language : en
Publisher: Springer Nature
Release Date : 2020-04-05
Introduction To Infinite Dimensional Systems Theory written by Ruth Curtain and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-05 with Science categories.
Infinite-dimensional systems is a well established area of research with an ever increasing number of applications. Given this trend, there is a need for an introductory text treating system and control theory for this class of systems in detail. This textbook is suitable for courses focusing on the various aspects of infinite-dimensional state space theory. This book is made accessible for mathematicians and post-graduate engineers with a minimal background in infinite-dimensional system theory. To this end, all the system theoretic concepts introduced throughout the text are illustrated by the same types of examples, namely, diffusion equations, wave and beam equations, delay equations and the new class of platoon-type systems. Other commonly met distributed and delay systems can be found in the exercise sections. Every chapter ends with such a section, containing about 30 exercises testing the theoretical concepts as well. An extensive account of the mathematical background assumed is contained in the appendix.
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 Linear Systems Theory
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Author : Ruth F. Curtain
language : en
Publisher: Springer
Release Date : 1978
Infinite Dimensional Linear Systems Theory written by Ruth F. Curtain and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Science categories.
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.
Stability And Stabilization Of Infinite Dimensional Systems With Applications
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Author : Zheng-Hua Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stability And Stabilization Of Infinite Dimensional Systems With Applications written by Zheng-Hua Luo 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 Computers categories.
This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robots arms and large space structures. Various control methods such as sensor feedback control and dynamic boundary control are applied to stabilize the equations. Many new theorems and methods are included in the book. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. New results on semigroups and their stability are presented, and readers can learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.