Introduction to the Calculus of Variations and Control with Modern Applications

John A. Burns (Autor)

Buch | Softcover

564 Seiten

2019
Chapman & Hall/CRC (Verlag)
978-0-367-37955-1 (ISBN)

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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.

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.

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.

Erscheinungsdatum	25.09.2019
Sprache	englisch
Maße	156 x 234 mm
Gewicht	453 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-367-37955-4 / 0367379554
ISBN-13	978-0-367-37955-1 / 9780367379551
Zustand	Neuware