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.
Preface
Part I : Calculus of Variations
Chapter 1 : Historical Notes on the Calculus of Variations
Chapter 2 : Introduction and Preliminaries
Chapter 3 : The Simplest Problem in the Calculus of Variations
Chapter 4 : Necessary Conditions for Local Minima
Chapter 5 : Sufficient Conditions for the Simplest Problem
Chapter 6 : Summary for the Simplest Problem
Chapter 7 : Extensions and Generalizations
Chapter 8 : Applications
Part II : Optimal Control
Chapter 9 : Optimal Control Problems
Chapter 10 : Simplest Problem in Optimal Control
Chapter 11 : Extensions of the Fundamental Maximum Principle
Chapter 12 : Linear Control Systems
Index
