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The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from the theoretical and design points of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability and stability. This theory is far more difficult for infinite-dimensional systems such as systems with time delay and distributed parameter systems. In the first place, the difficulty stems from the essential unboundedness of the system operator. Secondly, when control and observation are exercised through the boundary of the domain, the operator representing the sensor and actuator are also often unbounded.
The present book, in two volumes, is in some sense a self-contained account of this theory of quadratic cost optimal control for a large class of infinite-dimensional systems. Volume I deals with the theory of time evolution of controlled infinite-dimensional systems. It contains a reasonably complete account of the necessary semigroup theory and the theory of delay-differential and partial differential equations. Volume II deals with the optimal control of such systems when performance is measured via a quadratic cost. It covers recent work on the boundary control of hyperbolic systems and exact controllability. Some of the material covered here appears for the first time in book form.
The book should be useful for mathematicians and theoretical engineers interested in the field of control.
The present book, in two volumes, is in some sense a self-contained account of this theory of quadratic cost optimal control for a large class of infinite-dimensional systems. Volume I deals with the theory of time evolution of controlled infinite-dimensional systems. It contains a reasonably complete account of the necessary semigroup theory and the theory of delay-differential and partial differential equations. Volume II deals with the optimal control of such systems when performance is measured via a quadratic cost. It covers recent work on the boundary control of hyperbolic systems and exact controllability. Some of the material covered here appears for the first time in book form.
The book should be useful for mathematicians and theoretical engineers interested in the field of control.
"This book will undoubtedly prove [to be] a very valuable text to researchers familiar with finite-dimensional control theory and methods of functional analysis/semigroup theory who are interested in learning more about PDE systems and their control. This task is greatly facilitated by exploiting analogies with finite-dimensional theory and relying for the most part on operator/semigroup methods, thus reducing to a minimum the necessity of PDE background. The book presents, or refers to, the most recent and updated results in the field. For this reason, it should serve as an excellent asset to anyone pursuing a research career in the field." -Mathematical Reviews (Review of Volume II of the First Edition)
"We state at the outset that this book is a most welcome addition to the literature of this field, where it serves the need for a modern treatment on topics that only very recently have found a satisfactory solution. ...Many readers will appreciate the concise exposition.... The book makes a worthwhile effort to be accessible and relatively self-contained. [It] should prove to be a valuable source for mathematicians who want to learn more about aspects of deterministic control theory as well as theoretical engineers willing to learn the mathematical tools necessary to give precise formulations and solutions to problems arising from applications." -Mathematical Reviews (Review of Volume I of the First Edition)
"This is a book which people in the field have been waiting for since the late seventies.... The difference [in this book] lies in the scope of the classes of systems which are covered, which is much wider than that covered in earlier texts.... This book is a welcome addition to the literature. It presents a unified, up-to-date treatment of the main approaches to the representation of partial and differential delay systems.... The book is recommended both as anadvanced graduate text for mathematicians and as a valuable reference guide to the literature." -Journal of Mathematical Systems, Estimation, and Control (Review of Volume I of the First Edition)
"We state at the outset that this book is a most welcome addition to the literature of this field, where it serves the need for a modern treatment on topics that only very recently have found a satisfactory solution. ...Many readers will appreciate the concise exposition.... The book makes a worthwhile effort to be accessible and relatively self-contained. [It] should prove to be a valuable source for mathematicians who want to learn more about aspects of deterministic control theory as well as theoretical engineers willing to learn the mathematical tools necessary to give precise formulations and solutions to problems arising from applications." -Mathematical Reviews (Review of Volume I of the First Edition)
"This is a book which people in the field have been waiting for since the late seventies.... The difference [in this book] lies in the scope of the classes of systems which are covered, which is much wider than that covered in earlier texts.... This book is a welcome addition to the literature. It presents a unified, up-to-date treatment of the main approaches to the representation of partial and differential delay systems.... The book is recommended both as anadvanced graduate text for mathematicians and as a valuable reference guide to the literature." -Journal of Mathematical Systems, Estimation, and Control (Review of Volume I of the First Edition)
"I found myself browsing almost every time I looked in the book to work on the review, distracted by some exposition of one item or another of fascinating material...What is presented [in the work] is presented well, and I will continue to find the book valuable as a reference. Such a good treatment of this material is extremely welcome. That was indeed the case for the well-received original two-volume version of 1992-1993, and is now again the case for this second edition." -- Thomas I. Seidman, IEEE Control Systems Magazine (Review of the Second Edition)
"The monograph presents a broad review of the existing results in control theory of infinite-dimensional dynamical systems. Theoretical results are illustrated by many examples and additional comments. The monograph contains an extensive list of recent references concerning the theory of abstract linear systems. Finally, it should be pointed out that the monograph is the second edition of a two-volume monograph published by the same authors in 1993. Many results in the one-volume second edition are completely revised and corrected. Moreover, the second edition contains many new research results." -- Zentralblatt MATH (Review of the Second Edition)
"We state at the outset that this book is a most welcome addition to the literature of this field, where it serves the need for a modern treatment on topics that only very recently have found a satisfactory solution. ...Many readers will appreciate the concise exposition.... The book makes a worthwhile effort to be accessible and relatively self-contained. [It] should prove to be a valuable source for mathematicians who want to learn more about aspects of deterministic control theory as well as theoretical engineers willing to learn the mathematical tools necessary to give precise formulations and solutions to problems arising from applications." -- Mathematical Reviews (Review of Volume I of the First Edition)
"This book will undoubtedly prove [to be] a very valuable text to researchers familiar with finite-dimensional control theory and methods of functional analysis/semigroup theory who are interested in learning more about PDE systems and their control. This task is greatly facilitated by exploiting analogies with finite-dimensional theory and relying for the most part on operator/semigroup methods, thus reducing to a minimum the necessity of PDE background. The book presents, or refers to, the most recent and updated results in the field. For this reason, it should serve as an excellent asset to anyone pursuing a research career in the field." -- Mathematical Reviews (Review of Volume II of the First Edition)
"This is a book which people in the field have been waiting for since the late seventies.... The difference [in this book] lies in the scope of the classes of systems which are covered, which is much wider than that covered in earlier texts.... This book is a welcome addition to the literature. It presents a unified, up-to-date treatment of the main approaches to the representation of partial and differential delay systems.... The book is recommended both as an advanced graduate text for mathematicians and as a valuable reference guide to the literature." -- Journal of Mathematical Systems, Estimation, and Control (Review of Volume I of the First Edition)
"The monograph presents a broad review of the existing results in control theory of infinite-dimensional dynamical systems. Theoretical results are illustrated by many examples and additional comments. The monograph contains an extensive list of recent references concerning the theory of abstract linear systems. Finally, it should be pointed out that the monograph is the second edition of a two-volume monograph published by the same authors in 1993. Many results in the one-volume second edition are completely revised and corrected. Moreover, the second edition contains many new research results." -- Zentralblatt MATH (Review of the Second Edition)
"We state at the outset that this book is a most welcome addition to the literature of this field, where it serves the need for a modern treatment on topics that only very recently have found a satisfactory solution. ...Many readers will appreciate the concise exposition.... The book makes a worthwhile effort to be accessible and relatively self-contained. [It] should prove to be a valuable source for mathematicians who want to learn more about aspects of deterministic control theory as well as theoretical engineers willing to learn the mathematical tools necessary to give precise formulations and solutions to problems arising from applications." -- Mathematical Reviews (Review of Volume I of the First Edition)
"This book will undoubtedly prove [to be] a very valuable text to researchers familiar with finite-dimensional control theory and methods of functional analysis/semigroup theory who are interested in learning more about PDE systems and their control. This task is greatly facilitated by exploiting analogies with finite-dimensional theory and relying for the most part on operator/semigroup methods, thus reducing to a minimum the necessity of PDE background. The book presents, or refers to, the most recent and updated results in the field. For this reason, it should serve as an excellent asset to anyone pursuing a research career in the field." -- Mathematical Reviews (Review of Volume II of the First Edition)
"This is a book which people in the field have been waiting for since the late seventies.... The difference [in this book] lies in the scope of the classes of systems which are covered, which is much wider than that covered in earlier texts.... This book is a welcome addition to the literature. It presents a unified, up-to-date treatment of the main approaches to the representation of partial and differential delay systems.... The book is recommended both as an advanced graduate text for mathematicians and as a valuable reference guide to the literature." -- Journal of Mathematical Systems, Estimation, and Control (Review of Volume I of the First Edition)