Introduction to the Calculus of Variations and Control with Modern Applications

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.