Optimal Control

ISBN-13: 9780817649906 / Angielski / Miękka / 2010 / 500 str.

Richard Vinter

Opis

Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last several decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated with the Hamilton Jacobi equation. The book is largely self-contained and incorporates numerous simplifications and unifying features for the subject s key concepts and foundations. Features and Topics: * a comprehensive overview is provided for specialists and nonspecialists * authoritative, coherent, and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control * chapter coverage of dynamic programming and the regularity of minimizers * explains the necessary conditions for nonconvex problems This book is an excellent presentation of the foundations and applications of nonsmooth optimal control for postgraduates, researchers, and professionals in systems, control, optimization, and applied mathematics. --------------------------------- Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control. Mathematical Reviews This remarkable book presents Optimal Control seen as a natural development of Calculus of Variations so as to deal with the control of engineering devices Thanks to a great effort to be self-contained, this book] renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis). Automatica. The book may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicians, and it will be valued for its accessibility and clear exposition. Applications of Mathematics"

Recenzje

From the reviews:

"The book by R. Vinter is really well written; it goes from the very basic tools in variational analysis, as direct methods and regularity, to the most recent results in dynamic programming. Special attention is devoted to nonsmooth analysis tool ... . The book is enriched by many examples: this is a very important point for a reader who wants to approach Control Theory, and makes the volume suitable not only for specialists but also for students at a Ph. D. level." (zbMATH 0952.49001, 2021)

"In the book, many major developments in optimal control based on nonsmooth analysis in recent years are brought together in a form accessible to a broader audience.... The book may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicians, and it will be valued for its accessibility and clear exposition."-Applications of Mathematics

"In this self-contained monograph the author brings us right to the frontier of the research on necessary optimality conditions using the methodology of nonsmooth analysis and variational methods. He also presents a new perspective on the regularity of minimizers and discusses some of the recent progress on dynamic programming.... Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control." -Mathematical Reviews

"This remarkable book presents Optimal Control seen as a natural development of Calculus of Variations so as to deal with the control of engineering devices. This guideline is followed throughout the book and especially in its first chapter "Overview" that summarizes the philosophy, scope and results of this monograph. The main technical feature is the use of Nonsmooth Analysis and most of the attention is focused on necessary conditions for optimality...The book brings together most of recent developments in Optimal Control via Nonsmooth Analysis methods. Thanks to a great effort to be self-contained, it renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis)." -Automatica

"The book is strongly mathematically oriented and the author's focus is mostly on modern tools developed since the 1970s, namely nonsmooth variational analysis and differential inclusions. ... the opening chapter of this book can be considered as a major contribution to the modern optimal control literature. Together with the more advanced technical material of the other chapters, it turns this book into a valuable and by now classical source for systems control engineers and applied mathematicians." (Didier Henrion, Zentralblatt MATH, Vol. 1215, 2011)

Spis treści

Overview.- Measurable Multifunctions and Differential Inclusions.- Variational Principles.- Nonsmooth Analysis.- Subdifferential Calculus.- The Maximum Principle.- The Extended Euler–Lagrange and Hamilton Conditions.- Necessary Conditions for Free End-Time Problems.- The Maximum Principle for State Constrained Problems.- Necessary Conditions for Differential Inclusion Problems with State Constraints.- Regularity of Minimizers.- Dynamic Programming.

O autorze

Richard Vinter is Head of the Control and Power Research Group at Imperial College London.

Blurb

Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last several decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated with the Hamilton–Jacobi equation. The book is largely self-contained and incorporates numerous simplifications and unifying features for the subject’s key concepts and foundations.

Features and Topics:

* a comprehensive overview is provided for specialists and nonspecialists

* authoritative, coherent, and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control

* chapter coverage of dynamic programming and the regularity of minimizers

* explains the necessary conditions for nonconvex problems

This book is an excellent presentation of the foundations and applications of nonsmooth optimal control for postgraduates, researchers, and professionals in systems, control, optimization, and applied mathematics.

-----

Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control.—Mathematical Reviews

This remarkable book presents Optimal Control seen as a natural development of Calculus of Variations so as to deal with the control of engineering devices. ... Thanks to a great effort to be self-contained, it renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis). —Automatica

The book may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicians, and it will be valued for its accessibility and clear exposition.—Applications of Mathematics