Details

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.

<p><em>Optimal Control</em> 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&ndash;Jacobi equation. The book is largely self-contained and incorporates numerous simplifications and unifying features for the subject&rsquo;s key concepts and foundations.</p>
<p>Features and Topics:</p>
<p>* a comprehensive overview is provided for specialists and nonspecialists</p>
<p>* authoritative, coherent, and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control</p>
<p>* chapter coverage of dynamic programming and the regularity of minimizers</p>
<p>* explains the necessary conditions for nonconvex problems</p>
<p>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.</p>
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<p><em>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<strong>.</strong></em><strong>&mdash;Mathematical Reviews</strong></p>
<p><em>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).</em> <strong>&mdash;Automatica</strong></p>
<p><em>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.</em><strong>&mdash;Applications of Mathematics</strong></p>

Notes on each chapter delve into the history and development of the subject Self-contained, preparatory chapters included to minimize necessary prior knowledge Replete with examples to ground abstract theorems and ideas Includes supplementary material: sn.pub/extras

This new book brings together important new results and advances in optimal control, providing a self-contained analysis and incorporating numerous simplifications and unifying features for the subject'' key concepts and foundations.