Introduction To Infinite Dimensional Systems Theory

Author : Ruth F. Curtain,Hans Zwart
Publisher : Springer Science & Business Media
Page : 714 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242246

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An Introduction to Infinite-Dimensional Linear Systems Theory by Ruth F. Curtain,Hans Zwart Pdf

Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.

Author : Ruth Curtain,Hans Zwart
Publisher : Springer Nature
Page : 759 pages
File Size : 45,7 Mb
Release : 2020-04-05
Category : Science
ISBN : 9781071605905

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Introduction to Infinite-Dimensional Systems Theory by Ruth Curtain,Hans Zwart Pdf

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.

Author : R. F. Curtain,A. J. Pritchard
Publisher : Unknown
Page : 312 pages
File Size : 50,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662162571

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Infinite Dimensional Linear Systems Theory by R. F. Curtain,A. J. Pritchard Pdf

Author : Ruth F. Curtain,A. J. Pritchard
Publisher : Springer
Page : 320 pages
File Size : 55,7 Mb
Release : 1978
Category : Science
ISBN : UOM:39015000984677

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Infinite Dimensional Linear Systems Theory by Ruth F. Curtain,A. J. Pritchard Pdf

Author : Giuseppe Da Prato
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 47,7 Mb
Release : 2006-08-25
Category : Mathematics
ISBN : 9783540290216

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An Introduction to Infinite-Dimensional Analysis by Giuseppe Da Prato Pdf

Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.

Author : Birgit Jacob,Hans J. Zwart
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 40,8 Mb
Release : 2012-06-13
Category : Science
ISBN : 9783034803991

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Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces by Birgit Jacob,Hans J. Zwart Pdf

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.

Author : Igor' D. Čuešov,Igor Chueshov
Publisher : "Acta" publishers
Page : 421 pages
File Size : 42,6 Mb
Release : 2002
Category : Differentiable dynamical systems
ISBN : 9789667021641

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Introduction to the Theory of Infinite-dimensional Dissipative Systems by Igor' D. Čuešov,Igor Chueshov Pdf

Author : James C. Robinson
Publisher : Cambridge University Press
Page : 488 pages
File Size : 51,6 Mb
Release : 2001-04-23
Category : Mathematics
ISBN : 0521632048

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Infinite-Dimensional Dynamical Systems by James C. Robinson Pdf

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.

Author : Birgit Jacob,Hans Zwart
Publisher : Birkhäuser
Page : 220 pages
File Size : 53,8 Mb
Release : 2012-06-13
Category : Science
ISBN : 3034804008

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Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces by Birgit Jacob,Hans Zwart Pdf

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.

Author : Zheng-Hua Luo,Bao-Zhu Guo,Ömer Morgül
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781447104193

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Stability and Stabilization of Infinite Dimensional Systems with Applications by Zheng-Hua Luo,Bao-Zhu Guo,Ömer Morgül Pdf

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.

Author : Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 53,8 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387228969

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Dynamics in Infinite Dimensions by Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva Pdf

State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

Author : Alain Bensoussan,Giuseppe Da Prato,Michel C. Delfour,Sanjoy K. Mitter
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 44,9 Mb
Release : 2007-04-05
Category : Technology & Engineering
ISBN : 9780817645816

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Representation and Control of Infinite Dimensional Systems by Alain Bensoussan,Giuseppe Da Prato,Michel C. Delfour,Sanjoy K. Mitter Pdf

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.

Author : Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Publisher : Springer
Page : 916 pages
File Size : 44,9 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9783319530673

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Stochastic Optimal Control in Infinite Dimension by Giorgio Fabbri,Fausto Gozzi,Andrzej Święch Pdf

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.

Author : Neelacanta Sthanumoorthy
Publisher : Academic Press
Page : 512 pages
File Size : 47,9 Mb
Release : 2016-04-26
Category : Mathematics
ISBN : 9780128046838

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Introduction to Finite and Infinite Dimensional Lie (Super)algebras by Neelacanta Sthanumoorthy Pdf

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras

Author : Alain Bensoussan,Giuseppe Da Prato,Michel C. Delfour,Sanjoy K. Mitter
Publisher : Birkhäuser
Page : 0 pages
File Size : 46,5 Mb
Release : 2008-11-01
Category : Technology & Engineering
ISBN : 0817671153

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Representation and Control of Infinite Dimensional Systems by Alain Bensoussan,Giuseppe Da Prato,Michel C. Delfour,Sanjoy K. Mitter Pdf

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.