Math 5546

Calculus of Variations and Optimal Control

Course Description

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
  • Distributed Parameter Control
  • Computational Methods
  • 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 5546 - Calculus of Variations and Optimal Control - Spring 2015


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


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.

MATLAB is required for the computational exercises in this course. This can be purchased from the Software Distribution Office located in 3240 Torgerson Hall. Note that MATLAB is available on the computers at the Math Emporium. Use of any other software or programming languages is possible, but only after demonstrating adequacy and proficiency to the instructor.
Evaluation and Grading

There will be three in-class quizzes each worth 10% of the grade. The remainder of the grade will be determined from individual or group projects that include homework exercises and computational studies.

A final grade of 94% and higher will guarantee an A.

Honor Code

You are encouraged to discuss regular individual homework assignments with other members of the class, however any submitted write-up and code to be graded should be your work alone. Group projects should be worked on with only the group members. All quizzes 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.