Optimal Control (Systems & Control: Foundations & Applications)

__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**

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

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 "Optimal Control brings together many of the important advances in non-smooth optimal control of the last two decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated with the Hamilton-Jacobi equation. The analysis is largely self-contained and incorporates many of the simplifications and unifying features of optimal control revealed by recent research.". "This book is an essential resource for those who need to know about optimal control and its applications. Postgraduates, researchers, and professionals in systems science, control, optimization, and applied mathematics will benefit from its lucid exposition and the rich store of insights that it provides."--BOOK JACKET. Front Matter....Pages i-xix Overview....Pages 1-60 Measurable Multifunctions and Differential Inclusions....Pages 61-108 Variational Principles....Pages 109-126 Nonsmooth Analysis....Pages 127-177 Subdifferential Calculus....Pages 179-199 The Maximum Principle....Pages 201-231 The Extended Euler–Lagrange and Hamilton Conditions....Pages 233-284 Necessary Conditions for Free End-Time Problems....Pages 285-319 The Maximum Principle for State Constrained Problems....Pages 321-360 Necessary Conditions for Differential Inclusion Problems with State Constraints....Pages 361-396 Regularity of Minimizers....Pages 397-434 Dynamic Programming....Pages 435-491 Back Matter....Pages 493-507 This up-to-date reference brings together important advances in optimal control theory, many of which have not been previously published in book form. The presentation incorporates numerous unifying features of the theory and includes accessible proofs of key results. The introduction provides a non-technical summary of theorems and analytical techniques. The book will be a useful reference for engineers as well as a comprehensive introduction for researchers who are new to the field. Optimal Control emerged as a distinct field of research in the 1950s, to address in a unified fashion optimization problems arising in scheduling and the control of engineering devices, beyond the reach of traditional analytical and computational techniques.