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.
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