Optimal Control

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.

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

"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 tools.... 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."

-Zentralblatt Math

"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