Introduction to the Calculus of Variations and Control with Modern Applications
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Features
- Includes detailed proofs that illustrate how the underlying ideas are fundamental to the development of modern optimization and control theory
- Uses the maximum principle to rigorously develop the necessary conditions for more complex problems and for optimal control of linear systems
- Shows how optimal control problems are natural extensions of the classical calculus of variations to more complex problems
Summary
This book presents a rigorous introduction to variational calculus and optimal control, with a focus on function spaces of piecewise continuous and smooth functions. It shows how the calculus of variations can analyze optimization problems in functional analysis, optimal control, mechanics, and partial differential equations. It also illustrates how variational calculus provides the mathematical framework for a wide range of problems in engineering such as finite element analysis. The book provides readers with a sound understanding of the difference between necessary and sufficient conditions and when to use them.
Table of Contents
Part I 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. A Review of General Necessary Conditions. Applications. Part II Optimal Control: Optimal Control Problems. Simplest Problem in Optimal Control. Extensions of the Fundamental Maximum Principle. Linear Control Systems.
