## Math 5545

## Calculus of Variations and Optimal Control

From Catalog:

Unified course in the calculus of variations and control theory including multiple integral problems and distributed parameter control systems. Necessary conditions, sufficient conditions, nonclassical problems, optimal control, distributed parameter control, computational methods.

The first semester of this course develops the fundamental problem in the calculus of variations, necessary and sufficient conditions for extremal solutions.

- The Simplest Problem in the Calculus of Variations
- Necessary and Sufficient Conditions
- Free Endpoint Problems
- Extensions to Higher Dimensional Problems
- Extensions to Optimization

In the second semester (5546), we will discuss:

- The Simplest Problem in Optimal Control
- The Maximum Principle
- Linear Control Problems
- Introduction to Model Reduction Methods

Course Instructor: Jeff Borggaard

Regular office hours will be held in McBryde 528, times will be arranged at the first class meeting. Additional meeting times can be arranged by e-mail.

#### Course Resources

Selected reading material will be placed on reserve in the library.

This course will be managed using the Virginia Tech Scholar site.

#### Course Policy Sheet

Math 5545 - Calculus of Variations and Optimal Control - Fall 2014

##### Professor

Jeff Borggaard, regular office hours will be held in McBryde 528. Students are invited to e-mail me at (jborggaard@vt.edu) to arrange an appointment.

##### Text

Introduction to the Calculus of Variations and Control with Modern Applications, John A. Burns, 2013, Chapman and Hall/CRC Applied Mathematics and Nonlinear Science Series, (link to publisher page), as well as additional material.

##### Evaluation and Grading

Regular homework assignments constitute 20% of the grade. An in-class midterm and final exam will be worth 40% each.

##### Honor Code

You are encouraged to discuss regular homework assignments with other members of the class, however any submitted write-up and code to be graded should be your work alone. All exams (in-class and takehome) must be worked on independently.

Failure to follow these restrictions, and giving or receiving unauthorized aid or assistance on homework, in-class exams on the take-home final are Virginia Tech Honor System violations and cases will be filed.