Introduction to the Calculus of Variations and Control with Modern Applications
Auteur : Burns John A.
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions and discusses the importance of distinguishing between the necessary and sufficient conditions.
In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems.
By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.
Calculus of Variations: Historical Notes on the Calculus of Variations. Introduction and Preliminaries. The Simplest Problem in the Calculus of Variations. Necessary Conditions for Local Minima. Sufficient Conditions for the Simplest Problem. Summary for the Simplest Problem. Extensions and Generalizations. Applications. Optimal Control: Optimal Control Problems. Simplest Problem in Optimal Control. Extensions of the Fundamental Maximum Principle. Linear Control Systems.
John Burns is the Hatcher Professor of Mathematics, Interdisciplinary Center for Applied Mathematics at Virginia Polytechnic Institute and State University. He is a fellow of the IEEE and SIAM. His research interests include distributed parameter control; approximation, control, identification, and optimization of functional and partial differential equations; aero-elastic control systems; fluid/structural control systems; smart materials; optimal design; and sensitivity analysis.
Date de parution : 08-2013
15.6x23.4 cm
Date de parution : 09-2019
15.6x23.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 14 jours).
Prix indicatif 74,82 €
Ajouter au panierThèmes d’Introduction to the Calculus of Variations and Control... :
Mots-clés :
PWS; Optimal Control Problem; Admissible Controllers; Equality Constrained Optimization Problem; Linear Quadratic Optimal Control Problem; Strong Local Minimum; Weak Local Minimum; Piecewise Smooth Function; Optimal Control; Time Optimal Control Problem; Endpoint Conditions; Steers X0; Lagrange Multiplier Theorem; Brachistochrone Problem; Maximum Principle; Modern Optimal Control; Transversality Condition; Fundamental Lemmas; Weak Derivative; Adjoint Equation; Attainable Set; Initial Time T0; PWC; Optimal Pair; James Bernoulli